7 papers
Paths and Intersections: Minimum Realization of Okamura-Seymour Instances
Yu Chen, Pavlo Pylyavskyy, Zihan Tan
We study the inverse problem for shortest-path metrics of Okamura-Seymour (OS) instances. Given an OS metric on a cyclically ordered terminal set , the goal is to find minim…
Temperley-Lieb Immanants of Ribbon Decomposition Matrices
Son Nguyen, Pavlo Pylyavskyy
Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas…
Incidences, tilings, and fields
P. Pylyavskyy, M. Skopenkov
The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triang…
The dimer model and dynamical incidence geometry
Anton Izosimov, Pavlo Pylyavskyy
We propose a geometric counterpart of the dimer model on bipartite graphs. A state of our model consists of a choice of a point for each white vertex and hyperplane for each black…
Superport networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the…
Kirillov-Reshetikhin Dual Equivalence Graphs
Joseph McDonough, Pavlo Pylyavskyy, Shiyun Wang
Let be a tensor product of highest weight modules of corresponding to multiples of fundamental weights (i.e. rectangles). We consider three ways to stratify $…