Repositorio de producción científica de la Universidad de Sevilla

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

 

Advanced Search
 
Opened Access The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism
Cites
Show item statistics
Icon
Export to
Author: Martín Morales, Jorge
Falcón Ganfornina, Raúl Manuel
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2008
Document type: Presentation
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 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.
Cite: 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.
Size: 111.1Kb
Format: PDF

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

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 InternacionalAttribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)