Explicit enumeration formulas for m-regular simple stacks

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-13 DOI:10.1016/j.disc.2024.114317

Qianghui Guo , Yinglie Jin , Lisa Hui Sun , Hang Yang , Jie Yang

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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.

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多规则简单堆栈的显式枚举公式

对各种 RNA 二级结构和蛋白质接触图进行组合枚举，是组合学家和计算生物学家的重要兴趣所在。目前已经取得了许多成果，其中大部分是生成函数、递推公式或渐近公式，很少有明确的公式。本文主要研究与 m-regular 简单堆积相关的显式枚举公式，m-regular 简单堆积是 RNA 二级结构的经典组合模型。通过使用非交叉匹配和戴克路径理论，我们得到了m-正则简单堆积的显式枚举公式，并对弧线、发夹、分量和可见顶点进行了统计。这些结果可以还原为一些经典公式，如施密特和沃特曼关于 RNA 二级结构数的封闭式公式。此外，我们还研究了增强型 m-regular 简单堆栈的枚举，这是受蛋白质接触图研究的启发，其中两个末端顶点的度数上限被放宽为两个，从而得到了明确的公式。

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.