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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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| 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| _version_ | 1856543295631523840 |
|---|---|
| author | Agustín-Aquino, Octavio Alberto |
| author_facet | Agustín-Aquino, Octavio Alberto |
| author_sort | Agustín-Aquino, Octavio Alberto |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-07-24T22:56:15Z |
| description | 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. |
| first_indexed | 2025-12-02T15:25:36Z |
| format | Article |
| id | admjournalluguniveduua-article-156 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:36Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1562018-07-24T22:56:15Z Enumeration of strong dichotomy patterns Agustín-Aquino, Octavio Alberto strong dichotomy pattern, Pólya-Redfield theory, cyclic sieving 00A65, 05E18 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. Lugansk National Taras Shevchenko University 2018-07-25 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156 Algebra and Discrete Mathematics; Vol 25, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | strong dichotomy pattern Pólya-Redfield theory cyclic sieving 00A65 05E18 Agustín-Aquino, Octavio Alberto Enumeration of strong dichotomy patterns |
| title | Enumeration of strong dichotomy patterns |
| title_full | Enumeration of strong dichotomy patterns |
| title_fullStr | Enumeration of strong dichotomy patterns |
| title_full_unstemmed | Enumeration of strong dichotomy patterns |
| title_short | Enumeration of strong dichotomy patterns |
| title_sort | enumeration of strong dichotomy patterns |
| topic | strong dichotomy pattern Pólya-Redfield theory cyclic sieving 00A65 05E18 |
| topic_facet | strong dichotomy pattern Pólya-Redfield theory cyclic sieving 00A65 05E18 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156 |
| work_keys_str_mv | AT agustinaquinooctavioalberto enumerationofstrongdichotomypatterns |