8 papers · 1 filter
Locally anti-blocking -polytopes for flow polytopes
Jonah Berggren, Benjamin Braun, Alvaro Cornejo +6
Given an acyclic directed graph (DAG), the space of strength one flows is a lattice polytope called the flow polytope of the DAG. If the DAG admits an ample framing, then the flow…
-Tilings and Paths in
Zachery Peterson, Khrystyna Serhiyenko
An -tiling is a bi-infinite array of integers having all adjacent minors equal to one and all adjacent minors equal to zero. Introduced and st…
Consistent Dimer Models on Surfaces with Boundary
Jonah Berggren, Khrystyna Serhiyenko
A dimer model is a quiver with faces embedded in a surface. We define and investigate notions of consistency for dimer models on general surfaces with boundary which restrict to we…
D Farey graph, lambda lengths and -tilings
Anna Felikson, Oleg Karpenkov, Khrystyna Serhiyenko +1
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and -tilings. In particular, we prove a three-dimensional ve…
Leclerc's conjecture on a cluster structure for type A Richardson varieties
Khrystyna Serhiyenko, Melissa Sherman-Bennett
Leclerc constructed a conjectural cluster structure on Richardson varieties in simply laced types using cluster categories. We show that in type A, his conjectural cluster structur…
Triangulations, order polytopes, and generalized snake posets
Matias von Bell, Benjamin Braun, Derek Hanely +4
This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same r…