The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders

Williams, N.J. (2023) The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders. The Electronic Journal of Combinatorics, 30 (1): P1.29. ISSN 1077-8926

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Abstract

We prove the conjecture that the higher Tamari orders of Dimakis and Müller-Hoissen coincide with the first higher Stasheff–Tamari orders. To this end, we show that the higher Tamari orders may be conceived as the image of an order-preserving map from the higher Bruhat orders to the first higher Stasheff–Tamari orders. This map is defined by taking the first cross-section of a cubillage of a cyclic zonotope. We provide a new proof that this map is surjective and show further that the map is full, which entails the aforementioned conjecture. We explain how order-preserving maps which are surjective and full correspond to quotients of posets. Our results connect the first higher Stasheff–Tamari orders with the literature on the role of the higher Tamari orders in integrable systems.

Item Type:
Journal Article
Journal or Publication Title:
The Electronic Journal of Combinatorics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1700/1703
Subjects:
?? computational theory and mathematicsgeometry and topologytheoretical computer science ??
ID Code:
186717
Deposited By:
Deposited On:
16 Feb 2023 10:25
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 23:34