On the Permutations Generated by Cyclic Shift
Team of Mathematical Eco-Evolution
Ecole Normale Supérieure
The set of permutations generated by cyclic shift is studied using a
number system coding for these permutations. 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
structural and symmetry properties of the set of permutations ordered
according to generation by cyclic shift. The code is associated with an
Hamiltonian cycle in a regular weighted digraph. This Hamiltonian cycle
is conjectured to be of minimal weight, leading to a combinatorial Gray
code listing the set of permutations.
Full version: pdf,
(Concerned with sequences
Received September 21 2010;
revised version received December 13 2010; February 14 2011.
Published in Journal of Integer Sequences,
March 25 2011.
Journal of Integer Sequences home page