Geodesic
On the permutations generated by cyclic shift
Journal of integer sequences, Tome 14 (2011) no. 3.

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Summary: 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.
Classification : 05A05, 11A63, 05C20, 05C38
Keywords: permutations, cyclic shift, number system, palindrome, combinatorial gray code 
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     author = {Legendre, St\'ephane and Paclet, Philippe},
     title = {On the permutations generated by cyclic shift},
     journal = {Journal of integer sequences},
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     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a4/}
}
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Legendre, Stéphane; Paclet, Philippe. On the permutations generated by cyclic shift. Journal of integer sequences, Tome 14 (2011) no. 3. http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a4/