Algorithms for the Assignment and Transportation Problems

Qualitative Problems in Matrix Theory

A Partial Characterization of Poised Hermite–Birkhoff Interpolation Problems

Previous article Next article Complementarity Theorems for Linear ProgrammingA. C. WilliamsA. C. Williamshttps://doi.org/10.1137/1012015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Frank Eugene Clark, Mathematical Notes: Remark on the Constraint Sets in Linear Programming, Amer. Math. Monthly, 68 (1961), 351–352 MR1531192 0109.38204 CrossrefISIGoogle Scholar[2] A. J. Goldman, Resolution and separation theorems for polyhedral convex setsLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 41–51, in [4] MR0089113 0072.37505 Google Scholar[3] A. J. Goldman and , A. W. Tucker, Theory of linear programmingLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, 53–97, in [4] MR0101826 0072.37601 Google Scholar[4] H. W. Kuhn and , A. W. Tucker, Linear Inequalities and Related Systems, Princeton University Press, Princeton, 1956 0072.37502 Google Scholar[5] A. C. Williams, Boundedness relations for linear constraint sets, Linear Algebra and Appl., 3 (1970), 129–141 10.1016/0024-3795(70)90009-1 MR0266612 0201.22003 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Sparse solutions to an underdetermined system of linear equations via penalized Huber loss6 November 2020 | Optimization and Engineering, Vol. 22, No. 3 Cross Ref Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming26 February 2019 | Journal of Optimization Theory and Applications, Vol. 181, No. 3 Cross Ref Necessary and Sufficient Conditions for Noiseless Sparse Recovery via Convex Quadratic SplinesMustafa Ç Pinar12 February 2019 | SIAM Journal on Matrix Analysis and Applications, Vol. 40, No. 1AbstractPDF (416 KB)A labeling algorithm for the sensitivity ranges of the assignment problemApplied Mathematical Modelling, Vol. 35, No. 10 Cross Ref Bibliography15 August 2011 Cross Ref Sensitivity Analysis and Dynamic Programming15 February 2011 Cross Ref Bibliography Cross Ref Condition measures and properties of the central trajectory of a linear programMathematical Programming, Vol. 83, No. 1-3 Cross Ref New characterizations of ℓ1 solutions to overdetermined systems of linear equationsOperations Research Letters, Vol. 16, No. 3 Cross Ref Limiting behavior of weighted central paths in linear programmingMathematical Programming, Vol. 65, No. 1-3 Cross Ref Stability of linearly constrained convex quadratic programsJournal of Optimization Theory and Applications, Vol. 64, No. 1 Cross Ref Marginal values in mixed integer linear programmingMathematical Programming, Vol. 44, No. 1-3 Cross Ref A theory of linear inequality systemsLinear Algebra and its Applications, Vol. 106 Cross Ref Boundedness relations in linear semi-infinite programmingAdvances in Applied Mathematics, Vol. 8, No. 1 Cross Ref A Variable-Complexity Norm Maximization ProblemO. L. Mangasarian and T. -H. Shiau17 July 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 7, No. 3AbstractPDF (698 KB)Simple computable bounds for solutions of linear complementarity problems and linear programs26 February 2009 Cross Ref On polyhedral extension of some LP theoremsMathematical Programming, Vol. 30, No. 1 Cross Ref Polyhedral extensions of some theorems of linear programmingMathematical Programming, Vol. 24, No. 1 Cross Ref Optimal simplex tableau characterization of unique and bounded solutions of linear programsJournal of Optimization Theory and Applications, Vol. 35, No. 1 Cross Ref Projection and Restriction Methods in Geometric Programming and Related Problems Cross Ref Representation of Convex Sets Cross Ref Projection and restriction methods in geometric programming and related problemsJournal of Optimization Theory and Applications, Vol. 26, No. 1 Cross Ref The complementary unboundedness of dual feasible solution sets in convex programmingMathematical Programming, Vol. 12, No. 1 Cross Ref Theorems on the dimension of convex setsLinear Algebra and its Applications, Vol. 12, No. 1 Cross Ref On the primal and dual constraint sets in geometric programmingJournal of Mathematical Analysis and Applications, Vol. 32, No. 3 Cross Ref Volume 12, Issue 1| 1970SIAM Review History Submitted:23 December 1968Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012015Article page range:pp. 135-137ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Numerial Methods for Volterra Integral Equations with Singular Kernels

The Numerical Solution of Integral Equations on the Half-Line

Previous article Next article The Reduction of Certain Control Problems to an “Ordinary Differential” TypeJ. WargaJ. Wargahttps://doi.org/10.1137/1010036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails Stationarity conditions in optimal control problems class related to dynamical objects group control Cross Ref On the First- and Second-Order Conditions in Optimal Control Problems Related to Autonomous Objects Group lifecycle Cross Ref Optimal Control Problems with Time Delays: Constancy of the HamiltonianRichard B. Vinter25 July 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 4AbstractPDF (525 KB)On obtaining the stationarity conditions in an optimal control problem for a trajectory with a smooth contact with the phase boundary Cross Ref On one Method to Obtain Stationarity Conditions for an Optimal Control Problem Trajectory With a Smooth Boundary ContactIFAC-PapersOnLine, Vol. 51, No. 32 Cross Ref The Maximum Principle for Optimal Control Problems with Time DelaysA. Boccia and R. B. Vinter19 September 2017 | SIAM Journal on Control and Optimization, Vol. 55, No. 5AbstractPDF (407 KB)Problems with relaxed shifted controls and the pointwise maximum principleNonlinear Analysis: Theory, Methods & Applications, Vol. 75, No. 3 Cross Ref The Instability of Optimal Control Problems to Time DelayAlexey S. Matveev26 July 2006 | SIAM Journal on Control and Optimization, Vol. 43, No. 5AbstractPDF (340 KB)On the Characterization of Properly Relaxed Delayed ControlsJournal of Mathematical Analysis and Applications, Vol. 209, No. 1 Cross Ref Approximation of strongly relaxed minimizers with ordinary delayed controlsApplied Mathematics & Optimization, Vol. 32, No. 1 Cross Ref Jack Warga: In Appreciation14 July 2006 | SIAM Journal on Control and Optimization, Vol. 33, No. 2AbstractPDF (809 KB)Minimizing approximate original solutions for commensurate delayed controlsApplied Mathematics Letters, Vol. 7, No. 5 Cross Ref How to Properly Relax Delayed Controls Cross Ref A proper relaxation of shifted and delayed controlsJournal of Mathematical Analysis and Applications, Vol. 169, No. 2 Cross Ref Optimal controls and their discontinuities in quadratic problems of delay systemsIEEE Transactions on Automatic Control, Vol. 30, No. 7 Cross Ref Optimal Controls with PseudodelaysJ. Warga18 July 2006 | SIAM Journal on Control, Vol. 12, No. 2AbstractPDF (1227 KB)A conservative bound on the estimation error covariance matrix in the presence of correlated driving noise and correlated discrete measurement noiseJournal of Mathematical Analysis and Applications, Vol. 43, No. 2 Cross Ref References Cross Ref Volume 10, Issue 2| 1968SIAM Review History Submitted:18 October 1967Published online:18 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1010036Article page range:pp. 219-222ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Lower and Upper Bounds for the Number of Lattice Points in a SimplexAharon Gavriel Beged-dovAharon Gavriel Beged-dovhttps://doi.org/10.1137/0122012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. G. Beged-Dov, Some computational aspects of the P printers M paper mills trim problem, Business Administration, 2 (1970), 15–34 Google Scholar[2] P. C. Gilmore and , R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Res., 9 (1961), 849–859 MR0137589 0096.35501 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Homotopy techniques for solving sparse column support determinantal polynomial systemsJournal of Complexity, Vol. 66 Cross Ref Percolating sets in bootstrap percolation on the Hamming graphs and triangular graphsEuropean Journal of Combinatorics, Vol. 92 Cross Ref Polynomial Approximation of Anisotropic Analytic Functions of Several Variables16 July 2020 | Constructive Approximation, Vol. 51 Cross Ref Greedy approximations by signed harmonic sums and the Thue–Morse sequenceAdvances in Mathematics, Vol. 366 Cross Ref Sampling inequalities for anisotropic tensor product grids8 January 2019 | IMA Journal of Numerical Analysis, Vol. 107 Cross Ref Novel results for the anisotropic sparse grid quadratureJournal of Complexity, Vol. 47 Cross Ref On tensor product approximation of analytic functionsJournal of Approximation Theory, Vol. 207 Cross Ref Hyperbolic cross approximation in infinite dimensionsJournal of Complexity, Vol. 33 Cross Ref Rethinking the encounter probability for direct-to-target nuclear attacks for aviation security5 May 2011 | Journal of Transportation Security, Vol. 4, No. 3 Cross Ref Эффективные оценки производных обратной функцииИзвестия Российской академии наук. Серия математическая, Vol. 72, No. 4 Cross Ref Improved lower and upper bounds for the number of feasible solutions to a knapsaek problemOptimization, Vol. 19, No. 6 Cross Ref APPLICATION OF OPERATIONS RESEARCH IN PAPER PROCUREMENT Cross Ref The Number of Feasible Solutions to a Knapsack ProblemO. Achou12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 4AbstractPDF (209 KB)Bounds on the Number of Feasible Solutions to a Knapsack ProblemThomas A. Lambe12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 26, No. 2AbstractPDF (229 KB)The Paper Trim Problem: A Variable Demand AnalysisA I I E Transactions, Vol. 6, No. 1 Cross Ref A Remark on “an Inequality for the Number of Lattice Points in a Simplex”Manfred W. Padberg12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 20, No. 4AbstractPDF (253 KB) Volume 22, Issue 1| 1972SIAM Journal on Applied Mathematics History Submitted:09 December 1969Published online:12 July 2006 InformationCopyright © 1972 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0122012Article page range:pp. 106-108ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Previous article Full AccessCorrigendum: Discrete Time Stochastic Adaptive ControlGraham C. Goodwin, Peter J. Ramadge, and Peter E. CainesGraham C. Goodwin, Peter J. Ramadge, and Peter E. Caineshttps://doi.org/10.1137/0320063PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Corrigendum: Discrete Time Stochastic Adaptive Control." SIAM Journal on Control and Optimization, 20(6), p. 893 Previous article FiguresRelatedReferencesCited byDetails Robust Indirect Adaptive Control for a Class of Nonlinear Systems and Its Application to Shape Memory Alloy ActuatorsIEEE Access, Vol. 6 Cross Ref Asymptotic Behavior of Stochastic Systems Possessing Markovian RealizationsS. P. Meyn and P. E. Caines14 July 2006 | SIAM Journal on Control and Optimization, Vol. 29, No. 3AbstractPDF (2634 KB)Ergodic Theorems for Discrete Time Stochastic Systems Using a Stochastic Lyapunov FunctionSean P. Meyn14 July 2006 | SIAM Journal on Control and Optimization, Vol. 27, No. 6AbstractPDF (2969 KB)The Structural Robustness of Stochastic SystemsIFAC Proceedings Volumes, Vol. 21, No. 9 Cross Ref On the adaptive control of a class of systems with random parameters and disturbancesAutomatica, Vol. 21, No. 6 Cross Ref The self-tuning of stochastic adaptive pole placement controllers Cross Ref Volume 20, Issue 6| 1982SIAM Journal on Control and Optimization History Published online:17 February 2012 InformationCopyright © 1982 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0320063Article page range:pp. 893-893ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics

Previous article Full AccessErrata: Connection Formulas for Asymptotic Solutions of Second order Turning Points in Unbounded DomainsAnthony LeungAnthony Leunghttps://doi.org/10.1137/0506053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Errata: Connection Formulas for Asymptotic Solutions of Second order Turning Points in Unbounded Domains." SIAM Journal on Mathematical Analysis, 6(3), p. 600 Previous article FiguresRelatedReferencesCited byDetails Connection Formulas for Second-Order Differential Equations Having an Arbitrary Number of Turning Points of Arbitrary MultiplicitiesF. W. J. Olver17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 8, No. 4AbstractPDF (2573 KB)Connection Formulas for Second-Order Differential Equations with Multiple Turning PointsF. W. J. Olver17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 8, No. 1AbstractPDF (2418 KB) Volume 6, Issue 3| 1975SIAM Journal on Mathematical Analysis History Submitted:22 March 1974Published online:17 February 2012 InformationCopyright © 1975 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0506053Article page range:pp. 600-600ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics

Previous article Next article On Convergence of a Random Search Method in Convex Minimization ProblemsV. G. KarmanovV. G. Karmanovhttps://doi.org/10.1137/1119084PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. F. Dem'yanov and , A. M. Rubinov, Approximation Methods in Optimization Problems, American Elsevier, New York, 1970 0217.46203 Google Scholar[2] V. G. Karmanov, Estimates for the convergence of iteration methods of minimization, Ž. Vyčisl. Mat. i Mat. Fiz., 14 (1974), 3–14, 266, (Journal of Computational Mathematics and Mathematical Physics), (In Russian.) MR0341865 (49:6611) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Stochastic Three Points Method for Unconstrained Smooth MinimizationEl Houcine Bergou, Eduard Gorbunov, and Peter Richtárik1 October 2020 | SIAM Journal on Optimization, Vol. 30, No. 4AbstractPDF (985 KB)Optimization of Convex Functions with Random PursuitS. U. Stich, C. L. Müller, and B. Gärtner27 June 2013 | SIAM Journal on Optimization, Vol. 23, No. 2AbstractPDF (523 KB)Line search algorithms for adaptive filteringIEEE Transactions on Signal Processing, Vol. 41, No. 7 Cross Ref Volume 19, Issue 4| 1975Theory of Probability & Its Applications History Submitted:20 December 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119084Article page range:pp. 788-794ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Previous article Next article Second-Order Markov and Reciprocal Stationary Gaussian ProcessesR. N. MiroshinR. N. Miroshinhttps://doi.org/10.1137/1124099PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Bernshtei˘n, On the dependencies among random variablesCollected Works, Vol. IV, Nauka, Moscow, 1964, 235–254, (In Russian.) Google Scholar[2] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[3] Benton Jamison, Reciprocal processes: The stationary Gaussian case, Ann. Math. Statist., 41 (1970), 1624–1630 MR0267637 0248.60030 CrossrefGoogle Scholar[4] I. I. Gikhman and , A. V. Skorokhod, The Theory of Stochastic Processes, Vol. I, Springer-Verlag, New York, 1974 CrossrefGoogle Scholar[5] E. Kamke, Differentialgleichungen. Lösungsmethoden and Lösungen, Vol. 1, Chelsea, New York, 1974 Google Scholar[6] E. Wong, Some results concerning the zero-crossings of Gaussian noise, SIAM J. Appl. Math., 14 (1966), 1246–1254 10.1137/0114099 MR0207059 0147.15905 LinkGoogle Scholar[7] E. Wong, The distribution of intervals between zeros for a stationary Gaussian process, SIAM J. Appl. Math., 18 (1970), 67–73 10.1137/0118008 MR0256456 0221.60024 LinkGoogle Scholar[8] R. N. Miroshin, Convergence of Rice and Longuet-Higgins series for a Wong process, Theory Prob. Applications, 21 (1976), 863–866 10.1137/1121103 0374.60049 LinkGoogle Scholar[9] R. N. Miroshin, Asymptotics of the second factorial moment of the number of upward crossings of the line $kt+a$ by a Gaussian stationary process, Vestnik Leningrad. Univ., 23 (1968), 109–120 MR0235612 0165.52602 Google Scholar[10] M. Krein, Sur le problème du prolongement des fonctions hermitiennes positives et continues, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 17–22 MR0004333 0022.35302 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Characterization of Multivariate Stationary Gaussian Reciprocal DiffusionsJournal of Multivariate Analysis, Vol. 62, No. 1 Cross Ref Gaussian reciprocal diffusions and positive definite sturm-liouville operators4 April 2007 | Stochastics and Stochastic Reports, Vol. 55, No. 3-4 Cross Ref Gaussian reciprocal processes revisitedStatistics & Probability Letters, Vol. 12, No. 4 Cross Ref Reciprocal covariance solutions of some matrix differential equationsStochastic Processes and their Applications, Vol. 37, No. 1 Cross Ref Characterization and Classification of Gaussian Second Order Reciprocal Processes Cross Ref Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order2 May 2007 | Stochastics and Stochastic Reports, Vol. 34, No. 1-2 Cross Ref Reciprocal diffusions and stochastic differential equations of second order ∗Stochastics, Vol. 24, No. 4 Cross Ref Multivariate reciprocal stationary Gaussian processesJournal of Multivariate Analysis, Vol. 23, No. 1 Cross Ref On Miroshin’s Second-Order Reciprocal ProcessesJulia Abrahams3 August 2006 | SIAM Journal on Applied Mathematics, Vol. 44, No. 1AbstractPDF (316 KB)The Use of Rice SeriesR. N. Miroshin28 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (1011 KB)The zero-crossing problem for some nonstationary Gaussian processes (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 4 Cross Ref Convergence of Longuet-Higgins Series for Stationary Gaussian Markov Processes of First OrderR. N. Miroshin17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 1AbstractPDF (1546 KB) Volume 24, Issue 4| 1980Theory of Probability & Its Applications History Submitted:11 July 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124099Article page range:pp. 845-852ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

The purpose of this paper is to present numerical methods for the computation of samples of a Gaussian random process x(t) with prescribed autocorrelation or power spectral density.

Previous article Next article Sign Variations of the Macdonald IdentitiesDennis StantonDennis Stantonhttps://doi.org/10.1137/0517103PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractSign variations are given for the Macdonald identities for root systems of small rank. Limiting cases of these identities give properties of the eta function. Two such formulas are explicitly given.[1] Richard Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal., 11 (1980), 938–951 10.1137/0511084 82e:33002 0458.33002 LinkISIGoogle Scholar[2] F. Dyson, 1968, letter to L. Winquist, March Google Scholar[3] I. Macdonald, Affine root systems and Dedekind's $\eta$-function, Invent. Math., 15 (1972), 91–143 50:9996 0244.17005 CrossrefISIGoogle Scholar[4] I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal., 13 (1982), 988–1007 10.1137/0513070 84h:17006a 0498.17006 LinkISIGoogle Scholar[5] S. Milne, An elementary proof of the Macdonald identities for $A\sp {(1)}\sb l$, Adv. in Math., 57 (1985), 34–70 87e:17020 0586.33011 CrossrefISIGoogle Scholar[6] Lasse Winquist, An elementary proof of $p(11m+6)\equiv 0\,({\rm mod}\ 11)$, J. Combinatorial Theory, 6 (1969), 56–59 38:4434 0241.05006 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Leading coefficients of Morris type constant term identitiesAdvances in Applied Mathematics, Vol. 87 Cross Ref Logarithmic and Complex Constant Term Identities29 July 2013 Cross Ref A q-product Tutorial for a q-series Maple Package Cross Ref A New Proof of Winquist's IdentityJournal of Combinatorial Theory, Series A, Vol. 78, No. 2 Cross Ref Macdonald’s constant term conjectures for exceptional root systems1 January 1991 | Bulletin of the American Mathematical Society, Vol. 24, No. 2 Cross Ref A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q-Morris identityDiscrete Mathematics, Vol. 79, No. 3 Cross Ref The crank of partitions mod 8,9 and 101 January 1990 | Transactions of the American Mathematical Society, Vol. 322, No. 1 Cross Ref An Elementary Approach to the Macdonald Identities Cross Ref A Unified Approach to Macdonald’s Root-System ConjecturesDoron Zeilberger17 July 2006 | SIAM Journal on Mathematical Analysis, Vol. 19, No. 4AbstractPDF (2886 KB)First layer formulas for characters of 𝑆𝐿(𝑛,𝐶)1 January 1987 | Transactions of the American Mathematical Society, Vol. 299, No. 1 Cross Ref Volume 17, Issue 6| 1986SIAM Journal on Mathematical Analysis History Submitted:17 December 1984Accepted:16 September 1985Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0517103Article page range:pp. 1454-1460ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Random Partitions of SetsV. N. SachkovV. N. Sachkovhttps://doi.org/10.1137/1119019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Leo Moser and , Max Wyman, An asymptotic formula for the Bell numbers, Trans. Roy. Soc. Canada. Sect. III. (3), 49 (1955), 49–54 MR0078489 (17,1201c) 0066.31001 Google Scholar[2] V. N. Sachkov, Distribution of the number of distinct elements of a symmetric basis in a random $mA$-sample, Theory Prob. Applications, 16 (1971), 494–505 10.1137/1116053 0263.60002 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Combinatorial Models of the Distribution of Prime Numbers27 May 2021 | Mathematics, Vol. 9, No. 11 Cross Ref On the maximal multiplicity of block sizes in a random set partitionRandom Structures & Algorithms, Vol. 56, No. 3 Cross Ref Random partitions of a set with given number of blocksDiscrete Mathematics and Applications, Vol. 13, No. 3 Cross Ref Random Set Partitions: Asymptotics of Subset CountsJournal of Combinatorial Theory, Series A, Vol. 79, No. 2 Cross Ref Some Probabilistic Aspects of Set Partitions10 April 2018 | The American Mathematical Monthly, Vol. 104, No. 3 Cross Ref Random Set PartitionsWilliam M. Y. Goh and Eric Schmutz17 February 2012 | SIAM Journal on Discrete Mathematics, Vol. 7, No. 3AbstractPDF (1107 KB)On sets of integers with prescribed gapsMonatshefte f�r Mathematik, Vol. 116, No. 2 Cross Ref Gap-Free Set Partitions11 October 2006 | Random Structures & Algorithms, Vol. 3, No. 1 Cross Ref Generation of a random partition of a finite set by an urn modelJournal of Combinatorial Theory, Series A, Vol. 35, No. 2 Cross Ref Counting subsets of the random partition and the 'Brownian Bridge' processStochastic Processes and their Applications, Vol. 15, No. 2 Cross Ref Volume 19, Issue 1| 1974Theory of Probability & Its Applications History Submitted:14 February 1973Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119019Article page range:pp. 184-190ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics