Abstract
Given two families X and Y of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate a new class of polytopes is to take the intersection P = P 1 ∩ P 2 , where P 1 ∈ X , P 2 ∈ Y . Two basic questions then arise: 1) when P is integral and 2) whether P inherits the “old type” from P 1 , P 2 or has a “new type”, that is, whether P is unimodularly equivalent to a polytope in X ∪ Y or not. In this paper, we focus on the families of order polytopes and chain polytopes. Following the above framework, we create a new class of polytopes which are named order-chain polytopes. When studying their volumes, we discover a natural relation with Ehrenborg and Mahajan’s results on maximizing descent statistics.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
