Related papers: A Local Limit Theorem for Integer Partitions into …

Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…

We introduce a new type of partitions that consists of partitions whose different parts alternate in parity (e.g., $3+2+2+1+1$). Various properties of this partition function are studied. In particular, we obtain its asymptotic behavior by…

We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed,…

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…

This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.

A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.

We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…

Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as $h$-fixed points for an integer parameter $h$ by Hopkins and Sellers. Here, we…

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

Let A be a nonempty finite set of relatively prime positive integers, and let p_A(n) denote the number of partitions of n with parts in A. An elementary arithmetic argument is used to obtain an asymptotic formula for p_A(n).

We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…

Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identities, Euler's odd=distinct theorem, and the Andrews-Gordon…

We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of Hermitian random matrices. We obtain new estimates related to the local semi-circular…

A partition of a positive integer $n$ is a non-increasing sequence of positive integers which sum to $n$. A recently studied aspect of partitions is the minimal excludant of a partition, which is defined to be the smallest positive integer…

In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…

For positive integers $s$ and $L \geq 3$, Berkovich and Uncu (Ann. Comb. $23$ ($2019$) $263$--$284$) conjectured an inequality between the sizes of two closely related sets of partitions whose parts lie in the interval $\{s, \ldots, L+s\}$.…

This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…

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…