[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2021.61.2.409

Transformations of Partial Matchings

Nakamura, Inasa (Graduate School of Mathematical Sciences, The University of Tokyo)

Publication Information

Kyungpook Mathematical Journal / v.61, no.2, 2021 , pp. 409-439 More about this Journal

Abstract

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a partial matching, and the lattice polytope associated with a pair of lattice presentations, and we investigate transformations with minimal area.

Keywords

partial matching, chord diagram, lattice; polytope;

Citations & Related Records

Reference

1	I. Tinoco, Jr., O. C. Uhlenbeck and M. D. Levine, Estimation of secondary structure in ribonucleic acids, Nature Lond., 230(1971), 362-367. DOI
2	A. Barvinok, Integer points in polyhedra, Zurich Lectures in Advanced Mathematics, European Mathematical Society, 2008.
3	J. S. Birman, Braids, links and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press, Princeton, 1974.
4	W. Y. C. Chen, E. Y. P. Deng, R. R. X. Du, R. P. Stanley, and C. H. Yan, Crossings and nestings of matchings and partitions, Trans. Amer. Math. Soc., 359(2007), 1555-1575. DOI
5	E. Y. Jin, J. Qin and C. M. Reidys, Combinatorics of RNA structures with pseudoknots, Bull. Math. Biol., 70(2008), 45-67. DOI
6	E. Y. Jin and C. M. Reidys, Asymptotic enumeration of RNA structures with pseudoknots, Bull. Math. Biol., 70(2008), 951-970. DOI
7	R. Diestel, Graph theory, Graduate Texts in Mathematics 173, American Mathematical Society, Springer, 2010.
8	C. M. Reidys, Combinatorial computational biology of RNA, pseudoknots and neutral networks, Springer, New York, 2011.
9	M. Zuker and D. Sankoff, RNA secondary structures and their prediction, Bull. Math. Biol., 46(1984), 591-621. DOI
10	J. M. Pipas and J. E. McMahon, Method for predicting RNA secondary structure, Proc. Natn. Acad. Sci. USA, 72(1975), 2017-2021. DOI