Results 11 to 20 of about 863,417 (323)
Combinatorics and Statistical Mechanics of Integer Partitions [PDF]
Entropy, 2023 We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution
Themis Matsoukas
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Asymptotic formulas for integer partitions within the approach of microcanonical ensemble [PDF]
Condensed Matter Physics, 2012 The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions,
D. Prokhorov, A. Rovenchak
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Distribution of generalized mex-related integer partitions
Hardy-Ramanujan Journal, 2021 International audience The minimal excludant or "mex" function for an integer partition π of a positive integer n, mex(π), is the smallest positive integer that is not a part of π.
Kalyan Chakraborty, Chiranjit Ray
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Integer programming by partitioning [PDF]
ACM SIGMAP Bulletin, 1973 Integer Programming problems can be solved by a variety of methods. These can be grouped as follows:Complete EnumerationImplicit EnumerationBranch and BoundCutting PlanesPartitioningAsymptotic (or Group) TheoryConvex Analysis.The first two were discussed in educational series #2. This paper discusses the partitioning approach.
C. A. Haverly
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Integer Partitions and Binary Trees
Advances in Applied Mathematics, 2002 If \(\alpha\) is the 2-core, \((\beta_0,\beta_1)\) the 2-quotient of a partition \(\lambda\), then the triple \((\alpha; \beta_0,\beta_1)\) uniquely determines \(\lambda\); see \textit{G. James} and \textit{A. Kerber} [The representation theory of the symmetric group (Addison-Wesley, Reading, MA) (1981; Zbl 0491.20010)]. The present author constructs a
Frank Schmidt
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On the Distribution of Multiplicities in Integer Partitions [PDF]
Annals of Combinatorics, 2012 We study the distribution of the number of parts of given multiplicity (or equivalently, ascents of given size) in integer partitions. In this paper we give methods to compute asymptotic formulas for the expected value and variance of the number of parts of multiplicity d (d is a positive integer) in a random partition of a large integer n and also ...
D. Ralaivaosaona
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Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example [PDF]
Combinatorics, probability & computing, 2016 We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from asymptotically order ...
Richard Arratia, Stephen DeSalvo
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European Journal of Combinatorics, 2014 Let n be a positive integer and let g"1,...,g"n be real numbers. The following integer partition problem (IPP) is studied: find a partition of the integer [email protected]?"i"="1^[email protected][email protected]"i such that @?"i"="1^ng"[email protected][email protected]"i is maximal.
K. Engel, T. Radzik, J. Schlage-Puchta
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Separable Integer Partition Classes
Transactions of the American Mathematical Society, Series B, 2020 A classical method for partition generating function is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n n copies of n n are presented.
George E. Andrews
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Numerical Sets, Core Partitions, and Integer Points in Polytopes [PDF]
, 2017 We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope.
Hannah Constantin +2 more
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