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