Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$

Patrick Dehornoy; Emilie Tesson

Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$

Group Theory 2018-03-09 v2 Combinatorics

Authors: Patrick Dehornoy , Emilie Tesson

Abstract

On the model of simple braids, defined to be the left divisors of Garside's elements $\Delta\_n$ in the monoid $B\_\infty^+$ , we investigate simple elements in Thompson's monoid $F^+$ and in a larger monoid $H^+$ that is a hybrid of $B\_\infty^+$ and $F^+$ : in both cases, we count how many simple elements left divide the right lcm of the first n -- 1 atoms, and characterize their normal forms in terms of forbidden factors. In the case of $H^+$ , a generalized Pascal triangle appears.

Keywords

garside combinatorics thompson monoid braid monoid simple elements normal forms generalized pascal triangle

Cite

@article{arxiv.1803.02639,
  title  = {Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$},
  author = {Patrick Dehornoy and Emilie Tesson},
  journal= {arXiv preprint arXiv:1803.02639},
  year   = {2018}
}

Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$

Abstract

Keywords

Cite

Related papers