1 citations · 3 across the 13 of their papers we have counts for
13 papers
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…
A geometric perspective on the -cluster morphism category
Sibylle Schroll, Aran Tattar, Hipolito Treffinger +1
We show how the -cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that t…
A structural view of maximal green sequences
Mikhail Gorsky, Nicholas J. Williams
We study the structure of the set of all maximal green sequences of a finite-dimensional algebra. There is a natural equivalence relation on this set, which we show can be interpre…
The higher Stasheff--Tamari orders in representation theory
Nicholas J. Williams
We show that the relationship discovered by Oppermann and Thomas between triangulations of cyclic polytopes and the higher Auslander algebras of type , denoted , is a…
Stability spaces of string and band modules
Sibylle Schroll, Aran Tattar, Hipolito Treffinger +2
The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from consi…
Triangulations of prisms and preprojective algebras of type
Osamu Iyama, Nicholas J. Williams
We show that indecomposable two-term presilting complexes over , the preprojective algebra of , are in bijection with internal -simplices in the prism $Δ_{n} \time…
Quiver combinatorics for higher-dimensional triangulations
Nicholas J. Williams
We investigate the combinatorics of quivers that arise from triangulations of even-dimensional cyclic polytopes. Work of Oppermann and Thomas pinpoints such quivers as the prototyp…
The two higher Stasheff-Tamari orders are equal
Nicholas J. Williams
The set of triangulations of a cyclic polytope possesses two a priori different partial orders, known as the higher Stasheff-Tamari orders. The first of these orders was introduced…
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…
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…
The combinatorics of tensor products of higher Auslander algebras of type
Jordan McMahon, Nicholas J. Williams
We consider maximal non--intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in t…
Galois covers of type (p,...,p), vanishing cycles formula, and the existence of torsor structures
Mohamed Saidi, Nicholas Williams
In this article we prove a local Riemman-Hurwitz formula which compares the dimensions of the spaces of vanishing cycles in a finite Galois cover of type (p,p,...,p) between formal…
On the existence of a torsor structure for Galois covers over a complete discrete valuation ring
Mohamed Saidi, Nicholas Williams
In this note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $…