Qianghui Guo , Yinglie Jin , Lisa Hui Sun , Hang Yang , Jie Yang
{"title":"Explicit enumeration formulas for m-regular simple stacks","authors":"Qianghui Guo , Yinglie Jin , Lisa Hui Sun , Hang Yang , Jie Yang","doi":"10.1016/j.disc.2024.114317","DOIUrl":null,"url":null,"abstract":"<div><div>Combinatorial enumeration of various RNA secondary structures and protein contact maps is of significant interest for both combinatorialists and computational biologists. Numerous results have been obtained, most of which are in terms of generating functions, recurrences or asymptotic formulas, few are of explicit formulas. This paper is mainly concerned with finding explicit enumeration formulas related to <em>m</em>-regular simple stacks, a classic combinatorial model for RNA secondary structures. By using the theories of noncrossing matching and Dyck path, we obtain explicit enumeration formulas for <em>m</em>-regular simple stacks with statistics on arcs, hairpins, components and visible vertices. The results can reduce to some classic formulas like Schmitt and Waterman's closed form formula for the number of RNA secondary structures. Furthermore, we study the enumeration of enhanced <em>m</em>-regular simple stacks, stimulated by the study of protein contact maps, in which the upper bound of the degrees of the two terminal vertices is relaxed to two, explicit formulas are obtained.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114317"},"PeriodicalIF":0.7000,"publicationDate":"2024-11-13","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/S0012365X24004485","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
Combinatorial enumeration of various RNA secondary structures and protein contact maps is of significant interest for both combinatorialists and computational biologists. Numerous results have been obtained, most of which are in terms of generating functions, recurrences or asymptotic formulas, few are of explicit formulas. This paper is mainly concerned with finding explicit enumeration formulas related to m-regular simple stacks, a classic combinatorial model for RNA secondary structures. By using the theories of noncrossing matching and Dyck path, we obtain explicit enumeration formulas for m-regular simple stacks with statistics on arcs, hairpins, components and visible vertices. The results can reduce to some classic formulas like Schmitt and Waterman's closed form formula for the number of RNA secondary structures. Furthermore, we study the enumeration of enhanced m-regular simple stacks, stimulated by the study of protein contact maps, in which the upper bound of the degrees of the two terminal vertices is relaxed to two, explicit formulas are obtained.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
