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math.CO2023
A survey of congruences and quotients of partially ordered sets
Nicholas J. Williams
A quotient of a poset is a partial order obtained on the equivalence classes of an equivalence relation on ; is then called a congruence if it satisfies certain cond…
math.CO2020
The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders
Nicholas J. Williams
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 Tam…
math.CO2020
New interpretations of the higher Stasheff--Tamari orders
Nicholas J. Williams
In 1996, Edelman and Reiner defined the two higher Stasheff--Tamari orders on triangulations of cyclic polytopes and conjectured them to coincide. We open up an algebraic angle for…