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Mathematical proof demonstrates simplex face inequalities between chain and order polytopes for recursively constructed posets, generalizing prior geometric bounds.
In this paper, we study the simplex faces of the order polytope O(P) O ( P ) and the chain polytope C(P) C ( P ) of a finite poset P . We show that, if P can be recursively constructed from X X -free posets using disjoint unions and ordinal sums, then C(P) C ( P ) has at least as many k -dimensional simplex faces as O(P) O ( P ) does, for each dimension k . This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered.
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