Kyungpook Mathematical Journal

  • 제61권2호
  • /
  • Pages.409-439
  • /
  • 2021
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Transformations of Partial Matchings

  • Nakamura, Inasa (Graduate School of Mathematical Sciences, The University of Tokyo)
  • 투고 : 2017.05.26
  • 심사 : 2018.08.13
  • 발행 : 2021.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

The author would like to thank Professors Sigeo Ihara and Hiroki Kodama for their helpful comments.

참고문헌

  1. A. Barvinok, Integer points in polyhedra, Zurich Lectures in Advanced Mathematics, European Mathematical Society, 2008.
  2. J. S. Birman, Braids, links and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press, Princeton, 1974.
  3. 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. https://doi.org/10.1090/S0002-9947-06-04210-3
  4. R. Diestel, Graph theory, Graduate Texts in Mathematics 173, American Mathematical Society, Springer, 2010.
  5. E. Y. Jin, J. Qin and C. M. Reidys, Combinatorics of RNA structures with pseudoknots, Bull. Math. Biol., 70(2008), 45-67. https://doi.org/10.1007/s11538-007-9240-y
  6. E. Y. Jin and C. M. Reidys, Asymptotic enumeration of RNA structures with pseudoknots, Bull. Math. Biol., 70(2008), 951-970. https://doi.org/10.1007/s11538-007-9265-2
  7. J. M. Pipas and J. E. McMahon, Method for predicting RNA secondary structure, Proc. Natn. Acad. Sci. USA, 72(1975), 2017-2021. https://doi.org/10.1073/pnas.72.6.2017
  8. C. M. Reidys, Combinatorial computational biology of RNA, pseudoknots and neutral networks, Springer, New York, 2011.
  9. I. Tinoco, Jr., O. C. Uhlenbeck and M. D. Levine, Estimation of secondary structure in ribonucleic acids, Nature Lond., 230(1971), 362-367. https://doi.org/10.1038/230362a0
  10. M. Zuker and D. Sankoff, RNA secondary structures and their prediction, Bull. Math. Biol., 46(1984), 591-621. https://doi.org/10.1016/S0092-8240(84)80062-2