Generalizations of POD and PED partitions

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-16 DOI:10.1016/j.disc.2024.114150

Cristina Ballantine , Amanda Welch

引用次数: 0

Abstract

Partitions with even (respectively odd) parts distinct and all other parts unrestricted are often referred to as PED (respectively POD) partitions. In this article, we generalize these notions and study sets of partitions in which parts with fixed residue(s) modulo r are distinct while all other parts are unrestricted. We also study partitions in which parts divisible by r (respectively congruent to r modulo 2r) must occur with multiplicity greater than one.

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POD 和 PED 分区的一般化

通常把偶数（分别为奇数）部分不同而其他部分不受限制的分区称为 PED（分别为 POD）分区。在本文中，我们对这些概念进行了概括，并研究了这样一些分部集，在这些分部集中，具有固定残差的部分以 r 为模数是不同的，而所有其他部分都是不受限制的。我们还研究了这样的分部：其中可被 r 整除的部分（分别与 r 相等，模为 2r）必须以大于 1 的倍率出现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.