Presentation
The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism
Author/s | Martín Morales, Jorge
Falcón Ganfornina, Raúl Manuel |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Publication Date | 2008 |
Deposit Date | 2018-01-18 |
Abstract | 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 ... 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. |
Citation | 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. |
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