Séminaire Lotharingien de Combinatoire, 85B.6 (2021), 12 pp.

Nicholas J. Williams

The First Higher Stasheff-Tamari Orders Are Quotients of the Higher Bruhat Orders

Abstract. We study a map from the higher Bruhat orders to the first higher Stasheff-Tamari orders and show that it is a quotient map of posets. This resolves conjectures of Dimakis and Müller-Hoissen, and Danilov, Karzanov, and Koshevoy. This also requires further development of the theory of quotients of posets, as initiated by Hallam and Sagan. Our result reveals that the higher Stasheff-Tamari orders are connected with KP solitons and polygon equations.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

The following versions are available: