منابع مشابه
Two Poset Polytopes
Two convex polytopes, called the order polytope d)(P) and chain polytope <~(P), are associated with a finite poset P. There is a close interplay between the combinatorial structure of P and the geometric structure of E~(P). For instance, the order polynomial fl(P, m) of P and Ehrhart polynomial i(~9(P),m) of O(P) are related by f~(P,m+l)=i(d)(P),m). A "transfer map" then allows us to transfer p...
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Stanley (1986) showed how a finite partially ordered set gives rise to two polytopes, called the order polytope and chain polytope, which have the same Ehrhart polynomial despite being quite different combinatorially. We generalize his result to a wider family of polytopes constructed from a poset P with integers assigned to some of its elements. Through this construction, we explain combinator...
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We consider the complexity of determining the winner of a finite, two-level poset game. This is a natural question, as it has been shown recently that determining the winner of a finite, three-level poset game is PSPACE-complete. We give a simple formula allowing one to compute the status of a type of two-level poset game that we call parity-uniform. This class includes significantly more easil...
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We propose a separating-hyperplane algorithm for finding a nearest pair of points in two polytopes, where each polytope is expressed as the convex hull of given points in a Euclidian space. The proposed algorithm is an extension of the authors dual algorithm for finding t.he minimum-norm point in a polytope.
متن کاملTwo graph isomorphism polytopes
The convex hull ψn,n of certain (n!) 2 tensors was considered recently in connection with graph isomorphism. We consider the convex hull ψn of the n! diagonals among these tensors. We show: 1. The polytope ψn is a face of ψn,n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over ψn. 3. Optimization over ψn reduces to optimization over ψn,n. In particular, this i...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1986
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187680