Results 11 to 20 of about 4,436 (299)
Integer partitions detect the primes. [PDF]
Proc Natl Acad Sci U S AWe show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show that the primes are the solutions to special equations in partition functions. For example, an integer n ≥ 2 is prime if and only if
Craig W, van Ittersum JW, Ono K.
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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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Partitions of an Integer into Powers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results.
Matthieu Latapy
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Parallel Rank of Two Sandpile Models of Signed Integer Partitions [PDF]
Journal of Applied Mathematics, 2013 We introduce the concept of fundamental sequence for a finite graded poset X which is also a discrete dynamical model. The concept of fundamental sequence is a refinement of the concept of parallel convergence time for these models.
G. Chiaselotti +3 more
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Integer partitions probability distributions [PDF]
Communications in Statistics - Theory and Methods, 2019 Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when considering equally-likely random permutations on the set of $n$ letters.
Andrew V. Sills
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ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE [PDF]
Ural Mathematical Journal, 2023 An integer partition, or simply, a partition is a nonincreasing sequence \(\lambda = (\lambda_1, \lambda_2, \dots)\) of nonnegative integers that contains only a finite number of nonzero components. The length \(\ell(\lambda)\) of a partition \(\lambda\
Vitaly A. Baransky, Tatiana A. Senchonok
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Additive Integer Partitions in R [PDF]
Journal of Statistical Software, 2006 This paper introduces the partitions package of R routines, for numerical calculation of integer partititions. Functionality for unrestricted partitions, unequal partitions, and restricted partitions is provided in a small package that accompanies this ...
Robin K. S. Hankin
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Latin hypercubes realizing integer partitions [PDF]
Discrete Mathematics, 2023 For an integer partition $h_1 + \dots + h_n = N$, a 2-realization of this partition is a latin square of order $N$ with disjoint subsquares of orders $h_1,\dots,h_n$. The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to $m$-ary quasigroups, or, equivalently, latin hypercubes.
Diane Donovan, Tara Kemp, James Lefevre
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International Journal of Approximate Reasoning, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bernhard Ganter
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A phase transition in the distribution of the length of integer partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We assign a uniform probability to the set consisting of partitions of a positive integer $n$ such that the multiplicity of each summand is less than a given number $d$ and we study the limiting distribution of the number of summands in a random ...
Dimbinaina Ralaivaosaona
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