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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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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