English

Juggler's friezes

Combinatorics 2022-08-22 v1 Rings and Algebras

Abstract

This note generalizes SL(k)\mathrm{SL}(k)-friezes to configurations of numbers in which one of the boundary rows has been replaced by a ragged edge (described by a juggling function). We provide several equivalent definitions/characterizations of these juggler's friezes, in terms of determinants, linear recurrences, and a dual juggler's frieze. We generalize classic results, such as periodicity, duality, and a parametrization by part of a Grassmannian. We also provide a method of constructing such friezes from certain k×nk \times n matrices using the twist of a matrix.

Keywords

Cite

@article{arxiv.2208.09025,
  title  = {Juggler's friezes},
  author = {Roi Docampo and Greg Muller},
  journal= {arXiv preprint arXiv:2208.09025},
  year   = {2022}
}
R2 v1 2026-06-25T01:48:26.233Z