Geodesic
Enumeration of strong dichotomy patterns
Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 165-176.

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We apply the version of Pólya-Redfield theory obtained by White to count patterns with a given automorphism group to the enumeration of strong dichotomy patterns, that is, we count bicolor patterns of $\mathbb{Z}_{2k}$ with respect to the action of $\operatorname{Aff}(\mathbb{Z}_{2k})$ and with trivial isotropy group. As a byproduct, a conjectural instance of phenomenon similar to cyclic sieving for special cases of these combinatorial objects is proposed.
Keywords: strong dichotomy pattern, Pólya-Redfield theory, cyclic sieving. 
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Octavio A. Agustín-Aquino. Enumeration of strong dichotomy patterns. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 165-176. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a0/

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