Bipermutahedron and biassociahedron

TL;DR

This paper introduces a straightforward description of the face poset of biassociahedra, extending the known face descriptions of associahedra using planar trees, thereby enriching the combinatorial understanding of these polytopes.

Contribution

It provides a simple, generalized description of the face poset of biassociahedra, building on the combinatorial framework of associahedra.

Findings

Face poset of biassociahedra described explicitly

Generalization of associahedra face description achieved

Enhanced combinatorial understanding of biassociahedra

Abstract

We give a simple description of the face poset of the biassociahedra that generalizes, in a straightforward manner, the description of the faces of the Stasheff's associahedra via planar trees.