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arXiv:1007.2870 [math.CO]AbstractReferencesReviewsResources

The Number System of the Permutations Generated by Cyclic Shift

Stéphane Legendre

Published 2010-07-16, updated 2011-04-07Version 2

A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code describing the symmetry properties of the set of permutations generated by cyclic shift. This code is conjectured to be a combinatorial Gray code listing the set of permutations: this corresponds to an Hamiltonian path of minimal weight in an appropriate regular digraph.

Comments: 14 pages
Categories: math.CO
Subjects: 05A05
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