Computing the sets of totally symmetric and totally conjugate orthogonal partial Latin squares by means of a SAT solver
| Autor: | Falcón Ganfornina, Raúl Manuel, Falcón Ganfornina, Óscar Jesús, Núñez Valdés, Juan, Vigo Aguiar, Jesús (Coordinador) |
|---|---|
| Přispěvatelé: | Vigo Aguiar, Jesús, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. Departamento de Geometría y Topología, Universidad de Sevilla. FQM016: Códigos, Diseños, Criptografía y Optimización, Universidad de Sevilla. FQM326: Geometría Diferencial y Teoría de Lie |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | idUS. Depósito de Investigación de la Universidad de Sevilla instname |
| Popis: | Conjugacy and orthogonality of Latin squares have been widely studied in the literature not only for their theoretical interest in combinatorics, but also for their applications in distinct fields as experimental design, cryptography or code theory, amongst others. This paper deals with a series of binary constraints that characterize the sets of partial Latin squares of a given order for which their six conjugates either coincide or are all of them distinct and pairwise orthogonal. These constraints enable us to make use of a SAT solver to enumerate both sets. As an illustrative application, it is also exposed a method to construct totally symmetric partial Latin squares that gives rise, under certain conditions, to new families of Lie partial quasigroup rings. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|