Enumerating the Walecki‐Type Hamiltonian Cycle Systems |
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Authors: | Emanuele Brugnoli |
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Affiliation: | Department of Mathematics and Computer Sciences, University of Palermo, Palermo, Italy |
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Abstract: | Let be the complete graph on v vertices. A Hamiltonian cycle system of odd order v (briefly ) is a set of Hamiltonian cycles of whose edges partition the edge set of . By means of a slight modification of the famous of Walecki, we obtain 2n pairwise distinct and we enumerate them up to isomorphism proving that this is equivalent to count the number of binary bracelets of length n, i.e. the orbits of , the dihedral group of order 2n, acting on binary n‐tuples. |
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Keywords: | Hamiltonian cycle systems dihedral group integer compositions binary bracelets |
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