Enumeration of strong dichotomy patterns
Abstract
We apply the version of P\'olya-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 Z2k with respect to the action of (Z2k) 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.
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