Work

The $P$-Associahedron $f$-Vector Is a Comparability Invariant

Year: 2025

Type: article

Abstract: For any finite, connected poset $P$, we show that the $f$-vector of Galashin's $P$-associahedron $\mathscr A(P)$ only depends on the comparability graph of $P$. In particular, this allows us to produce a family of polytopes with the same $f$-vectors as permutohedra, but that are not combinatorially equivalent to permutohedra.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13422

Authors: Son Nguyen, Andrew Sack

Institutions: Massachusetts Institute of Technology, University of Michigan

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: G2923451624, Graduate Research Fellowship Program (GRFP), Totally Positive Spaces and Cluster Algebras, CAREER: Statistical mechanics and knot theory in algebraic combinatorics