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Rowmotion Orbits of Trapezoid Posets
Rowmotion is an invertible operator on the order ideals of a poset which has been extensively studied and is well understood for the rectangle poset. In this paper, we show that rowmotion is
An Expansion Formula for Decorated Super-Teichmüller Spaces
Motivated by the definition of super-Teichmüller spaces, and Penner–Zeitlin’s recent extension of this definition to decorated super-Teichmüller space, as examples of super Riemann surfaces, we use
Double Dimer Covers on Snake Graphs from Super Cluster Expansions
In a recent paper, the authors gave combinatorial formulas for the Laurent expansions of super λ-lengths in a marked disk, generalizing Schiffler’s T -path formula. In the present paper, we give an
Rooted Clusters for Graph LP Algebras
This work proves positivity for clusters of LP algebras by giving explicit formulas for each cluster variable and gives a combinatorial interpretation for these expansions using a generalization of T -paths.
A Lattice Model for Super LLT Polynomials
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock
We construct a family of generalized lattice models depending on a positive integer n whose partition functions are equal to the n-ribbon functions introduced by Lascoux, Leclerc and Thibon. Using
Arborescences of covering graphs
An arborescence of a directed graph $\Gamma$ is a spanning tree directed toward a particular vertex $v$. The arborescences of a graph rooted at a particular vertex may be encoded as a polynomial
1.1. Arborescences. Let Γ = (V,E,wt) be an edge-weighted quiver—that is, a directed multigraph with a function on the edges wt ∶ E → R, where R is some ring. We usually abbreviate “edge-weighted” to