The Number System of the Permutations Generated by Cyclic Shift

2010/07/16 by Legendre, Stéphane
#05A05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.2870

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.

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