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The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism

Opened Access The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism
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Autor: Martín Morales, Jorge
Falcón Ganfornina, Raúl Manuel
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I
Fecha: 2008
Tipo de documento: Ponencia
Resumen: There exists a bijection between the set of Latin squares of order n and the set of feasible solutions of the 3-dimensional planar assignment problem (3 PAPn). In this paper, we prove that, given a Latin square isotopism Θ, we can add some linear con-straints to the 3 PAPn in order to obtain a 1−1 correspondence between the new set offeasible solutions and the set of Latin squares of orden having Θ in their autotopism group. Moreover, we use Gröbner bases in order to describe an algorithm that allows one to obtain the cardinal of both sets.
Cita: Martín Morales, J. y Falcón Ganfornina, R.M. (2008). The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism. En XI Encuentro de Álgebra Computacional y Aplicaciones, Granada.
Tamaño: 111.1Kb
Formato: PDF

URI: https://hdl.handle.net/11441/69169

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