An inequality for anti-self-polar polytopes

TL;DR

This paper proves a conjectured inequality relating to the face vectors of anti-self-polar polytopes, using combinatorial methods rather than complex algebraic geometry.

Contribution

It establishes a new inequality for anti-self-polar polytopes' f-vectors, confirming a conjecture from 1989 with a combinatorial proof.

Findings

Proves an inequality for f-vectors of anti-self-polar polytopes

Uses combinatorial methods instead of algebraic geometry

Confirms a longstanding conjecture from 1989

Abstract

We prove an inequality for the f-vectors of anti-self-polar polytopes conjectured by Katz in 1989. The proof uses Kalai's combinatorial inequality based on a result of Whiteley. The inequality can also be obtained from the results of Stanley and Karu which however involve difficult algebraic geometry.