The Number System of the Permutations Generated by Cyclic Shift
Combinatorics
2011-04-08 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1007.2870,
title = {The Number System of the Permutations Generated by Cyclic Shift},
author = {Stéphane Legendre},
journal= {arXiv preprint arXiv:1007.2870},
year = {2011}
}
Comments
14 pages