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Computing the sets of totally symmetric and totally conjugate orthogonal partial Latin squares by means of a SAT solver

 

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Opened Access Computing the sets of totally symmetric and totally conjugate orthogonal partial Latin squares by means of a SAT solver
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Author: Falcón Ganfornina, Raúl Manuel
Falcón Ganfornina, Óscar Jesús
Núñez Valdés, Juan
Coordinator/Director: Vigo Aguiar, Jesús
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2017-07
Published in: 17th International Conference on Computational and Mathematical Methods in Science and Engineering (2017), p 841-852
ISBN/ISSN: 978-84-617-8694-7
Document type: Presentation
Abstract: 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.
Cite: Falcón Ganfornina, R.M., Falcón Ganfornina, Ó.J. y Núñez Valdés, J. (2017). Computing the sets of totally symmetric and totally conjugate orthogonal partial Latin squares by means of a SAT solver. En 17th International Conference on Computational and Mathematical Methods in Science and Engineering (841-852), Rota (Cádiz): Computational and Mathematical Methods in Science and Engineering.
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Format: PDF

URI: http://hdl.handle.net/11441/62076

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