منابع مشابه
Permutation Polytopes of Cyclic Groups
We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is...
متن کاملPermutation polytopes and indecomposable elements in permutation groups
Each group G of n × n permutation matrices has a corresponding permutation polytope, P (G) := conv(G) ⊂ R. We relate the structure of P (G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t, ⌊n/2⌋} is a sharp upper bound on the diameter of the graph of P (G). We also show that P (G) achieves its maximal dimension of (n − 1) precisely when G is 2-tra...
متن کاملOn the mean radius of permutation polytopes
Let X S n be a subset of the symmetric group S n and let Q X IR n 2 be the convex hull of the set of permutation matrices representing the elements of X in IR n 2. We present some formulas relating the cardinality of X and the maximal value of a typical linear function on Q X. Applications to the average case analysis of Combinatorial Optimization problems and to eecient counting are discussed.
متن کاملGeometry, Complexity, and Combinatorics of Permutation Polytopes
Each group G of permutation matrices gives rise to a permutation polytope P(G) = cony(G) c Re×d, and for any x ~ W, an orbit polytope P(G, x) = conv(G, x). A broad subclass is formed by the Young permutation polytopes, which correspond bijectively to partitions 2 = (21, ..., 2k)~-n of positive integers, and arise from the Young representations of the symmetric group. Young polytopes provide a f...
متن کاملPermutation polytopes corresponding to strongly supermodular functions
Throughout, let p be a positive integer and let be the set of permutations over {1; : : : ; p}. A real-valued function over subsets of {1; : : : ; p}, with (∅)=0, de7nes a mapping of into R where ∈ is mapped into the vector whose kth coordinate ( )k is the augmented -value obtained from adding k to the coordinates that precede it, according to the ranking induced by . The permutation polytope c...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2010
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/43/50/505306