Author

P. Pylyavskyy

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Preprint Oct 2026

Homomesy of Tropical $T$-systems: Finite Type

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 diagram, this system is periodic, as a special case of Zamolodchikov periodicity. In the associated tropical dynamics, every mutation along th...

Ariana Chin, P. Pylyavskyy · 0 citations

Preprint Sep 2026

Matrix-tree theorem for cohomological electrical networks

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 Dirichlet boundary condition, multiport condition, and prescribed voltage drops along nontrivial cycles on a surface. In this setting, we o...

P. Pylyavskyy, Svetlana Shirokovskikh, M. Skopenkov · 0 citations