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See detailDo the properties of an $S$-adic representation determine factor complexity?
Durand, Fabien; Leroy, Julien UL; Richomme, Gwenaël

in Journal of Integer Sequences (2013), 16(2), 132630

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See detailCounting non-isomorphic maximal independent sets of the n-cycle graph
Bisdorff, Raymond UL; Marichal, Jean-Luc UL

in Journal of Integer Sequences (2008), 11(5), 1-16

The number of maximal independent sets of the n-cycle graph C_n is known to be the nth term of the Perrin sequence. The action of the automorphism group of C_n on the family of these maximal independent ... [more ▼]

The number of maximal independent sets of the n-cycle graph C_n is known to be the nth term of the Perrin sequence. The action of the automorphism group of C_n on the family of these maximal independent sets partitions this family into disjoint orbits, which represent the non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets. We provide exact formulas for the total number of orbits and the number of orbits having a given number of isomorphic representatives. We also provide exact formulas for the total number of unlabeled (i.e., defined up to a rotation) maximal independent sets and the number of unlabeled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences. [less ▲]

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