Bounds on multiple self-avoiding polygons

Kyungpyo Hong, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A self-avoiding polygon is a lattice polygon consisting of a closed self-avoiding walk on a square lattice. Surprisingly little is known rigorously about the enumeration of self-avoiding polygons, although there are numerous conjectures that are believed to be true and strongly supported by numerical simulations. As an analogous problem to this study, we consider multiple self-avoiding polygons in a confined region as a model for multiple ring polymers in physics. We find rigorous lower and upper bounds for the number pm×n of distinct multiple self-avoiding polygons in the m × n rectangular grid on the square lattice. For m = 2, p2×n = 2n-1 - 1. And for integers m, n ≥ 3, (Equation presented)

Original languageEnglish
Pages (from-to)518-530
Number of pages13
JournalCanadian Mathematical Bulletin
Volume61
Issue number3
DOIs
Publication statusPublished - 2018 Sep

Keywords

  • Ring polymer
  • Self-avoiding polygon

ASJC Scopus subject areas

  • Mathematics(all)

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