A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns

Thorsten Holm; Peter Jorgensen

A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns

Combinatorics 2018-01-29 v3

Authors: Thorsten Holm , Peter Jorgensen

Abstract

Coxeter defined the notion of frieze pattern, and Conway and Coxeter proved that triangulations of polygons are in bijection with integral frieze patterns. We show a $p$ -angulated generalisation involving non-integral frieze patterns. We also show that polygon dissections give rise to even more general non-integral frieze patterns.

Keywords

frieze patterns p-angulated generalisation Conway and Coxeter theorem polygon dissections non-integral frieze patterns triangulations bijection

Cite

@article{arxiv.1709.09861,
  title  = {A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns},
  author = {Thorsten Holm and Peter Jorgensen},
  journal= {arXiv preprint arXiv:1709.09861},
  year   = {2018}
}

Comments

This is the final accepted version. It was accepted for publication by the International Mathematics Research Notices on 23/1-2018. 14 pages

A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns

Abstract

Keywords

Cite

Comments

Related papers