Derangements on the n-cube
نویسندگان
چکیده
منابع مشابه
Derangements on the n-cube
Chen, W.Y.C. and R.P. Stanley, Derangements on the n-cube, Discrete Mathematics 115 (1993) 65-15. Let Q. be the n-dimensional cube represented by a graph whose vertices are sequences of O’s and l’s of length n, where two vertices are adjacent if and only if they differ only at one position. A k-dimensional subcube or a k-face of Q. is a subgraph of Q. spanned by all the vertices u1 u2 u, with c...
متن کاملFinite Groups of Derangements on the n-Cube II
Given k ∈ N and a finite group G, it is shown that G is isomorphic to a subgroup of the group of symmetries of some n-cube in such a way that G acts freely on the set of k-faces, if and only if, gcd(k, |G|) = 2s for some non-negative integer s. The proof of this result is existential but does give some ideas on what n could be.
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W. Y. C. Chen and R. P. Stanley have characterized the symmetries of the n-cube that act as derangements on the set of k-faces. In this paper we aim to use their result to characterize those finite subgroups of symmetries whose non-trivial members are derangements of the set of k-faces.
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In this paper we present a method for analyzing a general class of random Ž . walks on the n-cube and certain subgraphs of it . These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to Ž . guarantee that the resulting distrib...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90479-d