A1 Refereed original research article in a scientific journal
Packing of permutations into Latin squares
Authors: Foldes Stephan, Kaszanyitzky András, Major László
Publisher: Elsevier B.V.
Publication year: 2021
Journal: Discrete Applied Mathematics
Journal name in source: Discrete Applied Mathematics
Volume: 297
First page : 102
Last page: 108
ISSN: 0166-218X
eISSN: 1872-6771
DOI: https://doi.org/10.1016/j.dam.2021.03.001
Web address : https://doi.org/10.1016/j.dam.2021.03.001
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/57558493
For every positive integer n greater than 4 there is a set of Latin squares of order n such that every permutation of the numbers 1, . . . , n appears exactly once as a row, a column, a reverse row or a reverse column of one of the given Latin squares. If n is greater than 4 and not of the form p or 2p for some prime number p congruent to 3 modulo 4, then there always exists a Latin square of order n in which the rows, columns, reverse rows and reverse columns are all distinct permutations of 1, . . . , n, and which constitute a permutation group of order 4n. If n is prime congruent to 1 modulo 4, then a set of (n − 1) / 4 mutually orthogonal Latin squares of order n can also be constructed by a classical method of linear algebra in such a way, that the rows, columns, reverse rows and reverse columns are all distinct and constitute a permutation group of order n (n − 1).
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