Enumeration of strong dichotomy patterns

• Date: 2018
• Main Author: Agustín-Aquino, Octavio Alberto
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: strong dichotomy pattern; Pólya-Redfield theory; cyclic sieving; 00A65; 05E18
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156
• Journal Title: Algebra and Discrete Mathematics

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...