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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
References:
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
Document Type: Article
MSC: 00A65, 05E18
Language: English
Citation: Octavio A. Agustín-Aquino, “Enumeration of strong dichotomy patterns”, Algebra Discrete Math., 25:2 (2018), 165–176
Citation in format AMSBIB
\Bibitem{Agu18}
\by Octavio~A.~Agust{\'\i}n-Aquino
\paper Enumeration of strong dichotomy patterns
\jour Algebra Discrete Math.
\yr 2018
\vol 25
\issue 2
\pages 165--176
\mathnet{http://mi.mathnet.ru/adm652}
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