Vertaisarvioitu alkuperäisartikkeli tai data-artikkeli tieteellisessä aikakauslehdessä (A1)
Packing of permutations into Latin squares
Julkaisun tekijät: Foldes Stephan, Kaszanyitzky András, Major László
Kustantaja: Elsevier B.V.
Julkaisuvuosi: 2021
Journal: Discrete Applied Mathematics
Tietokannassa oleva lehden nimi: Discrete Applied Mathematics
Volyymi: 297
Aloitussivu: 102
Lopetussivun numero: 108
ISSN: 0166-218X
eISSN: 1872-6771
DOI: http://dx.doi.org/10.1016/j.dam.2021.03.001
Verkko-osoite: https://doi.org/10.1016/j.dam.2021.03.001
Rinnakkaistallenteen osoite: 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).
Ladattava julkaisu This is an electronic reprint of the original article. |