Garside combinatorics for Thompson’s monoid $F^+$ and a hybrid with the braid monoid $B_{\infty }^{+}$

Abstract

On the model of simple braids, defined to be the left divisors of Garside's elements Δ n in the monoid B ∞ + , we investigate simple elements in Thompson's monoid F + and in a larger monoid H + that is a hybrid of B ∞ + 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.

Locations

• Algebraic Combinatorics - View - PDF
• arXiv (Cornell University) - View - PDF
• French digital mathematics library (Numdam) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
• Algebraic Combinatorics - View - PDF
• DataCite API - View