Permutation polytopes and indecomposable elements in permutation groups
نویسندگان
چکیده
منابع مشابه
Permutation 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...
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By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2006
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.11.004