Kalai's flag conjecture for locally anti-blocking polytopes

TL;DR

This paper proves Kalai's full flag conjecture for locally anti-blocking polytopes, establishing conditions for equality and characterizing when the polytope is a generalized Hanner polytope.

Contribution

The authors prove Kalai's flag conjecture for a new class of polytopes and characterize the equality case as generalized Hanner polytopes.

Findings

Kalai's flag conjecture holds for locally anti-blocking polytopes.

Equality in the conjecture occurs if and only if the polytope is a generalized Hanner polytope.

The result extends the understanding of the combinatorial structure of these polytopes.

Abstract

We prove Kalai's full flag conjecture for the class of locally anti-blocking polytopes, and show that there is equality if and only if the polytope is a (generalized) Hanner polytope.