{"title":"Generalizations of POD and PED partitions","authors":"Cristina Ballantine , Amanda Welch","doi":"10.1016/j.disc.2024.114150","DOIUrl":null,"url":null,"abstract":"<div><p>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 <em>r</em> are distinct while all other parts are unrestricted. We also study partitions in which parts divisible by <em>r</em> (respectively congruent to <em>r</em> modulo 2<em>r</em>) must occur with multiplicity greater than one.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"347 11","pages":"Article 114150"},"PeriodicalIF":0.7000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24002814","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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。
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.
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