Results 271 to 280 of about 4,436 (299)

Diagonal Sequences of Integer Partitions

Summary: Let \(\mathcal{P}(n)\) be the set of partitions of the positive integer \(n\). For \(\alpha = (\alpha_1, \dots, \alpha_t) \in \mathcal{P}(n)\) define the diagonal sequence \(\delta(\alpha) = (d_k(\alpha))_{k \geq 1}\) via \(d_k(\alpha) = |\{i\mid 1 \leq i \leq k\text{ and }\alpha_i + i - 1 \geq k\}|\). We show that the set of all partitions in
Neubauer, Michael, Vargas, Harmony
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Integer Partition

2023
Yung-Hsiang Lu, George K. Thiruvathukal
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The “best” partition of an integer

BIT, 1974
An algorithm, based on a conjecture, to compute a permutation whose repeated application to a given set will yield a maximum number of different orderings of that set is presented. The algorithm gives the lengths of the cycles required. This problem turns out to be equivalent to the problem of determining a partitionB(n) ofn for which the least common ...
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Stationary Random Partitions of Positive Integers

Theory of Probability & Its Applications, 2000
Let \(S_n,n\geq 1\), and \(S_\infty\) denote the symmetric group of degree \(n\) and the infinite symmetric group, respectively. Let \(S^\infty\) denote the space of all coherent sequences of permutations endowed with the topology of the projective limit of the \(S_n\), \(n\geq 1\). A Borel probability measure on \(S^\infty\) is called central if it is
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Partition theory of integers

2013
This chapter is aimed at studying generating functions in their application to the theory of integer partitions. Historically, this area marks the beginning of modern combinatorics in the form of a very large number discoveries mainly by Euler and later by many others such as Gauss, Jacobi, Sylvester and Ramanujan.
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Partition of Integers

ACM Transactions on Mathematical Software, 1976
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Integer Partitions

2021
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Dyson's crank and the mex of integer partitions

Journal of Combinatorial Theory - Series A, 2022
Brian Hopkins
exaly  

Multi-lump wave patterns of KPI via integer partitions

Physica D: Nonlinear Phenomena, 2023
Sarbarish Chakravarty
exaly  

Partitions of Integers

2022
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