相关论文: On Andrews' partitions with parts separated by par…

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…

In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between "the sum of the numbers of distinct members in the partitions of a positive integer $n$" and…

Euler's theorem asserts that $A(n)=B(n)$ where $A(n)$ is the number of partitions of $n$ into distinct parts and $B(n)$ is the number of partitions of $n$ into odd parts. In this paper, it is proved that for $n>0$, \begin{align*}…

Partition regularity over algebraic structures is a topic in Ramsey theory that has been extensively researched by combinatorialists. Motivated by recent work in this area, we investigate the computability-theoretic and reverse-mathematical…

In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's Theorem. We show that this identity is a straightforward consequence of the classical result. We also…

This paper gives a bijective proof of Andrews' refinement of the Alladi-Schur theorem. Moreover, it demonstrates that the bijective framework introduced here can be used to reproduce and provide a bijective account of Andrews' recursive…

In this article, we first investigate the partitions whose parts are congruent to $a$ or $b$ modulo $k$ with the aid of separable integer partition classes with modulus $k$ introduced by Andrews. Then, we introduce the…

An introductory to generalized parton distributions is given which emphasizes their spectral property and its uses as well as the equivalence of various GPD representations. Furthermore, the status of the theory and phenomenology of hard…

E394 in the Enestrom index. Translated from the Latin original, "De partitione numerorum in partes tam numero quam specie datas" (1768). Euler finds a lot of recurrence formulas for the number of partitions of $N$ into $n$ parts from some…

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 $\{s, \ldots, L+s\}$.…

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of $\overline{\mathcal{EO}}(n)$ and further prove that $\overline{\mathcal{EO}}(n)\equiv0\pmod4$ for…

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial coefficients. We follow…

A cubic partition consists of partition pairs $(\lambda,\mu)$ such that $\vert\lambda\vert+\vert\mu\vert=n$ where $\mu$ involves only even integers but no restriction is placed on $\lambda$. This paper initiates the notion of generalized…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to…

In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…

We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…

We extend recent results by G. E. Andrews and G. Simay on the $m$th largest and $m$th smallest parts of a partition to the more general context of skew plane partitions. In order to do this, we introduce new objects called skew plane…