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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.RT2023
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…
math.RT2023
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…