相关论文: Shifted and Shiftless Partition Identities II

This paper is concerned with a class of partition functions $a(n)$ introduced by Radu and defined in terms of eta-quotients. By utilizing the transformation laws of Newman, Schoeneberg and Robins, and Radu's algorithms, we present an…

Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this atricle, we will investigate six types of partitions from the view of the point of separable integer partition classes.

This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form $2^k-1$ for some integer k. Such partitions have potential applications in cryptography, specifically in distributed…

This work follows the spirit of Andrews' series of papers on Partition Analysis. In $2011$, Savage and Sills found new sum sides for the little G\"ollnitz identities and provided their partition interpretations. It turns out that similar…

A partition of a positive integer $n$ is defined as a non-increasing sequence $P = [y_0, y_1, ..., y_m]$ of positive integers which sum to $n$, where the $y_i$ are called the $parts$ of the partition. A Young diagram is a visual…

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…

The number of parts in the partitions (resp. distinct partitions) of $n$ with parts from a set were considered. Its generating functions were obtained. Consequently, we derive several recurrence identities for the following functions: the…

Consideration of a classification of the number of partitions of a natural number according to the members of sub-partitions differing from unity leads to a non-recursive formula for the number of irreducible representations of the…

Almost nothing is known about the parity of the partition function $p(n)$, which is conjectured to be random. Despite this expectation, Ono surprisingly proved the existence of infinitely many linear dependence congruence relations modulo 4…

In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which provide a witness to the divisibility properties of $p(5n+4),$…

We deduce from the strong form of the Hardy--Ramanujan asymptotics for the partition function $p(n)$ an asymptotics for $p_{-S}(n)$, the number of partitions of $n$ that do not use parts from a finite set $S$ of positive integers. We apply…

It is well known that the number of partitions into distinct even parts equals the number of $4$-regular partitions. In this paper we prove identities relating certain restricted partitions into distinct even parts with restricted…

A number of recent papers have estimated ratios of the partition function $p(n-j)/p(n)$, which appears in many applications. Here, we prove an easy-to-use effective bound on these ratios. Using this, we then study second shifted difference…

We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and…

Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…

A partition is a $\bar{s}$-core if it is the result of removing all of the $s$-bars from a partition. We extend a method of Olsson and Bessenrodt to determine the number of even partitions that are simultaneously $\bar{s}$-core and…

We give a possible explanation for the mystery of a missing number in the statement of a problem that asks for the non-negative integers to be partitioned into three subsets. We interpret the missing number as one of the clues that can lead…

Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer…

In this paper we present a new class of integer partition identities. The number of partitions with d-distant parts can be represented as a sum of the number of partitions with 1-distant parts whose even parts are greater than twice the…

This paper is an annotated list of transformation properties and identities satisfied by the four theta functions $\theta _1$, $\theta _2$, $\theta _3$, $\theta _4$ of one complex variable, presented in a ready-to-use form. An attempt is…