Enumeration of strong dichotomy patterns

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...

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Bibliographic Details
Date:2018
Main Author: Agustín-Aquino, Octavio Alberto
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary: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.