Kalai's flag conjecture for locally anti-blocking polytopes

2025/07/29 by Chor, Arnon
#52B05 (Primary) #52B15 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2507.22284

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.

Citations

• On the illumination of 1-symmetric convex bodies
• Godbersen's conjecture for locally anti-blocking bodies
• Kalai's 3^d conjecture for unconditional and locally anti-blocking polytopes
• Volume growth of Funk geometry and the flags of polytopes
• A note on Kalai's 3^d Conjecture
• Complement reducible graphs

Related

• Kalai's 3^d conjecture for unconditional and locally anti-blocking polytopes
• Convex polytopes and linear algebra
• On the Size of Equifacetted Semi-Regular Polytopes
• Face numbers of centrally symmetric polytopes from split graphs
• Linear inequalities for flags in graded posets