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A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
- Source :
- AIMS Mathematics, Vol 6, Iss 1, Pp 261-295 (2021), idUS. Depósito de Investigación de la Universidad de Sevilla, instname, idUS: Depósito de Investigación de la Universidad de Sevilla, Universidad de Sevilla (US)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five. Junta de Andalucía FQM-016
- Subjects :
- Class (set theory)
critical set
Enumeration
Mathematics::General Mathematics
General Mathematics
Order up to
Structure (category theory)
enumeration
Combinatorics
Set (abstract data type)
cycle structure
Latin square
Mathematics
Autotopism
Mathematics::Combinatorics
Group (mathematics)
Cycle structure
lcsh:Mathematics
Mathematics::History and Overview
Census
lcsh:QA1-939
autotopism
latin square
Critical set
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....5867e8217a73fab9dde2d1fb86062bed