Séminaire Lotharingien de Combinatoire, 91B.43 (2024), 12 pp.
Son Nguyen and Andrew Sack
On The f-Vectors of Poset Associahedra
Abstract.
For any finite connected poset P, Galashin introduced a simple
convex
(|P|-2)-dimensional polytope A(P) called the poset associahedron. First, we show that the f-vector of A(P) only depends on the comparability graph of P.
Additionally, for a family of posets called broom posets, whose poset
associahedra interpolate between permutohedra and associahedra, we
give a simple combinatorial interpretation of the h-vector. The
interpretation relates to the theory of stack-sorting and allows us to
prove the real-rootedness of some of their h-polynomials.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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