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math.CO2025
Facial nested complexes and acyclonestohedra
Chiara Mantovani, Arnau Padrol, Vincent Pilaud
We study nested complexes of building sets on the Las Vergnas face lattices of oriented matroids. Such a nested complex is the face lattice of an oriented matroid, obtained by iter…
math.CO2024
Pivot polytopes of products of simplices and shuffles of associahedra
Vincent Pilaud, Germain Poullot
We provide a piecewise linear isomorphism from the normal fan of the pivot polytope of a product of simplices to the normal fan of a shuffle of associahedra.
math.CO2023
Posets for -polynomials in cluster algebras from surfaces
Vincent Pilaud, Nathan Reading, Sibylle Schroll
We prove a simple formula for arbitrary cluster variables in the marked surfaces model. As part of the formula, we associate a labeled poset to each tagged arc, such that the assoc…