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math.CO2026
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…
math.CO2026
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…
math.CO2026
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…