The Rise-Contact involution on Tamari intervals
Viviane Pons
TL;DR
This paper introduces an involution on Tamari and m-Tamari intervals that swaps specific statistics, confirming a conjecture about the structure of these intervals.
Contribution
It presents a new involution that proves an open conjecture regarding the symmetry of statistics on Tamari intervals.
Findings
The involution swaps 'rises' and 'contacts' statistics.
It confirms the conjecture by Prévillé-Ratelle.
Provides a combinatorial proof of the symmetry.
Abstract
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 Pr\'eville-Ratelle on intervals of the m-Tamari lattice.
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