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math.CO2026
Matrix Formulae and Skein Relations for Quasi-Cluster Algebras
Cody Gilbert, McCleary Philbin, Kayla Wright
In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formul…
math.CO2025
Local Statistics of the -Dimer Model
Nickolas Anderson, Moriah Elkin, Elizabeth Kelley +2
The classical dimer model is concerned with the (weighted) enumeration of perfect matchings of a graph. An -dimer cover is a multiset of edges that can be realized as the disjoi…
math.CO2024
Twists of Gr(3,n) Cluster Variables as Double and Triple Dimer Partition Functions
Moriah Elkin, Gregg Musiker, Kayla Wright
We give a combinatorial interpretation for certain cluster variables in Grassmannian cluster algebras in terms of double and triple dimer configurations. More specifically, we exam…