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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LetD = (V (D), A(D)) be a digraph. The competition graph ofD, is the graphwith vertex set V (D) and edge set {uv ∈ ( V (D) 2 ) : ∃w ∈ V (D), uw, vw ∈ A(D)}. The double competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ ( V (D) 2 )
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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.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2017
ISSN: 0895-4801,1095-7146
DOI: 10.1137/16m1091800