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Published on: December 22, 2020
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Zigzag stacks and m-regular linear stacks
William Y C Chen1, Qiang-Hui Guo, Lisa H Sun
11 Center for Combinatorics, The Key Laboratory of Pure Mathematics and Combinatorics of Ministry of Education of China and Tianjin Key Laboratory of Combinatorics (LPMC-TJKLC), Nankai University , Tianjin, P.R. China .
Summary
This study introduces m-regular linear stacks, generalizing RNA secondary structures. We derive a generating function and asymptotic formulas for counting these structures, providing new insights into graph decomposition and RNA folding.
Area of Science:
- Computational Biology
- Graph Theory
- Bioinformatics
Background:
- Protein contact maps can be represented as graphs, decomposable into stacks and queues.
- RNA secondary structures are specific types of stacks with constraints on vertex degree and arc length.
- Previous work established formulas and algorithms for RNA secondary structures and extended versions.
Purpose of the Study:
- To generalize the concept of RNA secondary structures to m-regular linear stacks.
- To derive a generating function for m-regular linear stacks for any m >= 2.
- To establish recurrence relations and asymptotic formulas for counting these structures.
Main Methods:
- Utilized a reduction operation to transform m-regular linear stacks into m-reduced zigzag stacks.
- Derived an equation for the generating function of m-reduced zigzag stacks.
- Transferred the generating function equation to m-regular linear stacks.
Main Results:
- Obtained a general equation for the generating function of m-regular linear stacks for m >= 2.
- Deduced a recurrence relation for the number of m-regular linear stacks on n vertices.
- Derived an asymptotic formula for the count of m-regular linear stacks.
Conclusions:
- The study provides a comprehensive mathematical framework for analyzing m-regular linear stacks.
- The derived formulas and relations offer new tools for understanding graph structures related to RNA.
- This work extends previous findings on RNA secondary structures and their combinatorial properties.
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