منابع مشابه
Cyclic Derangements
A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem to enumerating derangements in the wreath product of any finite cyclic group with the symmetric group. We also give qand (q, t)-analogs for cy...
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We introduce the notion of a graph derangement, which naturally interpolates between perfect matchings and Hamiltonian cycles. We give a necessary and sufficient condition for the existence of graph derangements on a locally finite graph. This result was first proved by W.T. Tutte in 1953 by applying some deeper results on digraphs. We give a new, simple proof which amounts to a reduction to th...
متن کاملOn Parallel Generation of Partial Derangements, Derangements and Permutations
The concept of a partial derangement is introduced and a versatile representation of partial derangements is proposed with permutations and derangements as special cases. The representation is derived from a representation of permutations by iterative decomposition of symmetric permutation group Sn into cosets. New algorithms are proposed for generation of partial set derangements in t. The con...
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In this note, we present two new identities for derangements. As a corrolary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.
متن کاملGray code for derangements
We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no 0xed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of 0xed points bounded between two constants. ? 2003 Elsevier B.V. All rights...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/435