The Rise-Contact involution on Tamari intervals

Viviane Pons (1)

1 GALaC - LRI - Graphes, Algorithmes et Combinatoire (LRI)

We describe an involution on Tamari intervals and m-Tamari intervals. This involution switches two sets of statistics known as the "rises" and the "contacts" and so proves an open conjecture from Préville-Ratelle on intervals of the m-Tamari lattice.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Viviane Pons. The Rise-Contact involution on Tamari intervals. The Electronic Journal of Combinatorics, 2019. ⟨hal-02145887⟩