English

Generating series of cyclically fully commutative elements is rational

Combinatorics 2016-12-13 v1

Abstract

In this paper, we study the generating function of cyclically fully commutative elements in Coxeter groups, which are elements such that any cyclic shift of theirs reduced decompositions remains a reduced expression of a fully commutative element. By designing a finite state automaton recognizing reduced expressions of cyclically fully commutative elements, we can show that the aforementioned generating series is always rational.

Keywords

Cite

@article{arxiv.1612.03764,
  title  = {Generating series of cyclically fully commutative elements is rational},
  author = {Mathias Pétréolle},
  journal= {arXiv preprint arXiv:1612.03764},
  year   = {2016}
}

Comments

16 pages, 4 figures

R2 v1 2026-06-22T17:20:53.576Z