Enumeration of strong dichotomy patterns

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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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
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-156
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua: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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-07-24T22:56:15Z
collection OJS
language English
topic strong dichotomy pattern
Pólya-Redfield theory
cyclic sieving
00A65
05E18
spellingShingle strong dichotomy pattern
Pólya-Redfield theory
cyclic sieving
00A65
05E18
Agustín-Aquino, Octavio Alberto
Enumeration of strong dichotomy patterns
topic_facet strong dichotomy pattern
Pólya-Redfield theory
cyclic sieving
00A65
05E18
format Article
author Agustín-Aquino, Octavio Alberto
author_facet Agustín-Aquino, Octavio Alberto
author_sort Agustín-Aquino, Octavio Alberto
title Enumeration of strong dichotomy patterns
title_short 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_sort enumeration of strong dichotomy patterns
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.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/156
work_keys_str_mv AT agustinaquinooctavioalberto enumerationofstrongdichotomypatterns
first_indexed 2025-07-17T10:30:06Z
last_indexed 2025-07-17T10:30:06Z
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