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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
doaj   +6 more sources

Integer partitions detect the primes [PDF]

Proceedings of the National Academy of Sciences
Significance Integer partitions arise naturally in additive number theory, algebraic geometry, combinatorics, mathematical physics, and representation theory. We have identified a surprising role for partitions in multiplicative number theory.
William Craig, Jan-Willem M. van Ittersum, Ken Ono   +2 more
semanticscholar   +5 more sources

Maximum entropy and integer partitions [PDF]

Combinatorial Theory, 2020
We derive asymptotic formulas for the number of integer partitions with given sums of $j$th powers of the parts for $j$ belonging to a finite, non-empty set $J \subset \mathbb N$. The method we use is based on the `principle of maximum entropy' of Jaynes.
Gweneth McKinley, Marcus Michelen, Will Perkins   +2 more
semanticscholar   +7 more sources

Integer Partitions and Exclusion Statistics [PDF]

Journal of Physics A: Mathematical and Theoretical, 2007
We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $ p=0$ is a
Alain Comtet, Andrews G E, Andrews G E, Anghel D V, Comtet A Majumdar S N Ouvry S Sabhapandit S, Leinaas J M, Pasquier V, Polychronakos A P, Satya N Majumdar, Stéphane Ouvry, Szekeres G, Szekeres G, Temperley H N Y   +12 more
core   +6 more sources

Strongly intersecting integer partitions [PDF]

Discrete Mathematics, 2014
We call a sum a1+a2+• • •+ak a partition of n of length k if a1, a2, . . . , ak and n are positive integers such that a1 ≤ a2 ≤ • • • ≤ ak and n = a1 + a2 + • • • + ak. For i = 1, 2, . . . , k, we call ai the ith part of the sum a1 + a2 + • • • + ak. Let
Borg, Peter
core   +2 more sources

Partitions and sums of integers with repetition

Journal of Combinatorial Theory, Series A, 1979
AbstractA partition of N is called “admissible” provided some cell has arbitrarily long arithmetic progressions of even integers in a fixed increment. The principal result is that the statement “Whenever {Ai}i < r is an admissible partition of N, there are some i < r and some sequence 〈xn〉n < ω of distinct members of N such that xn + xm ϵ Ai whenever ...
Neil Hindman
openalex   +4 more sources

Gluing two affine Yangians of 𝔤𝔩1

Journal of High Energy Physics, 2019
We construct a four-parameter family of affine Yangian algebras by gluing two copies of the affine Yangian of 𝔤𝔩1. Our construction allows for gluing operators with arbitrary (integer or half integer) conformal dimension and arbitrary (bosonic or ...
Wei Li, Pietro Longhi
doaj   +3 more sources

Parallel Rank of Two Sandpile Models of Signed Integer Partitions

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, T. Gentile, G. Marino, P. A. Oliverio   +3 more
doaj   +2 more sources

Generalized Integer Partitions, Tilings of Zonotopes and Lattices

, 2000
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory.
BA Davey, E George, E Goles, GD Bailey, Guy David Bailey, Günter Ziegler, M Latapy, M Latapy, N Destainville, Nicolas Destainville, Richard Kenyon, Serge Elnitsky, T Brylawski   +12 more
core   +5 more sources

Integer Partitions with Fixed Subsums [PDF]

The Electronic Journal of Combinatorics, 2005
Given two positive integers $m\le n$, we consider the set of partitions $\lambda=(\lambda_1,\dots,\lambda_\ell,0,\dots)$, $\lambda_1\ge\lambda_2\ge\dots$, of $n$ such that the sum of its parts over a fixed increasing subsequence $(a_j)$ is $m$: $\lambda_{a_1}+\lambda_{a_2}+\dots=m$. We show that the number of such partitions does not depend on $n$ if $
Yu. V. Yakubovich
openalex   +5 more sources