4 papers · 1 filter
Cluster Expansions from Punctured Orbifolds
Esther Banaian, Wonwoo Kang, Elizabeth Kelley +2
We provide multiple combinatorial expansion formulas - in terms of snake graphs, labelled posets, matrices, and -walks - for elements in generalized cluster algebras associated…
Higher -Continued Fractions and Dimers on Band Graphs
Wonwoo Kang, Yucong Lei
In this paper, we explore the theory of higher dimers on band graphs. First, we provide a combinatorial interpretation for the trace of the -deformed higher continued fraction m…
Unimodality and Cluster Algebras from Surfaces
Wonwoo Kang, Kyeongjun Lee, Eunsung Lim
We prove that the rank polynomial of the lattice of order ideals of a loop fence poset is unimodal. This poset arises as the poset of join-irreducibles in the lattice of good match…
Skein relations for punctured surfaces
Esther Banaian, Wonwoo Kang, Elizabeth Kelley
We investigate skein relations in cluster algebras from punctured surfaces, extending the work of Çanakçi-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinator…