{"title":"Oriented posets, rank matrices and q-deformed Markov numbers","authors":"Ezgi Kantarcı Oğuz","doi":"10.1016/j.disc.2024.114256","DOIUrl":null,"url":null,"abstract":"<div><p>We define <em>oriented posets</em> with corresponding <em>rank matrices</em>, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets. As an application, we give a combinatorial model for <em>q</em>-deformed Markov numbers. We also resolve a conjecture of Leclere and Morier-Genoud and give several identities between circular rank polynomials.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114256"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-12","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/S0012365X2400387X","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
We define oriented posets with corresponding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets. As an application, we give a combinatorial model for q-deformed Markov numbers. We also resolve a conjecture of Leclere and Morier-Genoud and give several identities between circular rank polynomials.
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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