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Pré-Publication, Document De Travail Année : 2018

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

Résumé

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.
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Dates et versions

hal-01723604 , version 1 (05-03-2018)
hal-01723604 , version 2 (08-03-2018)

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Patrick Dehornoy, Emilie Tesson. Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B_\infty^+$. 2018. ⟨hal-01723604v2⟩
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