|
Algebra and Discrete Mathematics, 2018, Volume 25, Issue 2, Pages 165–176
(Mi adm652)
|
|
|
|
RESEARCH ARTICLE
Enumeration of strong dichotomy patterns
Octavio A. Agustín-Aquino Universidad Tecnológica de la Mixteca, Instituto de Física y Matemáticas, Carretera a Acatlima Km. 2.5, Huajuapan de León, Oaxaca, México, C.P. 69000
Abstract:
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 Z2k with respect to the action of Aff(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.
Keywords:
strong dichotomy pattern, Pólya-Redfield theory, cyclic sieving.
Received: 03.02.2016 Revised: 01.02.2018
Citation:
Octavio A. Agustín-Aquino, “Enumeration of strong dichotomy patterns”, Algebra Discrete Math., 25:2 (2018), 165–176
Linking options:
https://www.mathnet.ru/eng/adm652 https://www.mathnet.ru/eng/adm/v25/i2/p165
|
Statistics & downloads: |
Abstract page: | 137 | Full-text PDF : | 102 | References: | 40 |
|