25 citations · 225 across the 54 of their papers we have counts for
49 papers · 1 filter
Homomesy of Tropical -systems: Finite Type
Ariana Chin, Pavlo Pylyavskyy
In 2007, Fomin and Zelevinsky introduced the bipartite belt, a sequence of bipartite cluster mutations whose exchange relations form a discrete dynamical system. For each Dynkin di…
Matrix-tree theorem for cohomological electrical networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We introduce a new type of boundary condition for electrical networks by specifying a cohomology class on the underlying cell complex. As special and limiting cases, we recover the…
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…
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…
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 $…
Correlations in random cluster model at
Son Nguyen, Pavlo Pylyavskyy
Let be a measure that samples a subset of a finite ground set, and let be the event that element is sampled. The measure is negatively correlated if for…