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math-ph2026
Cohomology for solutions of polygon equations
Serban Matei Mihalache, Tomoro Mochida
Polygon equations form a family of equations generalizing the pentagon equation. In this paper, we construct semi-simplicial sets of permitted colorings associated with set-theoret…
math-ph2026
Constructing Solutions of Simplex Equations from Polygon Equations
Serban Matei Mihalache, Tomoro Mochida
We study polygon equations and their connections to simplex equations, which generalize the pentagon and Yang-Baxter equations, respectively. First, we show that certain ''commutat…