Proof of Gal's conjecture for the D series of generalized associahedra

TL;DR

This paper proves Gal's conjecture for D series generalized associahedra, showing they are not nestohedra for n > 3, and confirms the conjecture's validity for these polytopes.

Contribution

It establishes Gal's conjecture for D series generalized associahedra and clarifies their structural properties as simple flag polytopes.

Findings

Gal's conjecture holds for D series generalized associahedra

These polytopes are not nestohedra for n > 3

The polytopes are simple flag polytopes

Abstract

In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture holds for them.