dc.contributor.author
Boyadzhiyska, Simona
dc.contributor.author
Das, Shagnik
dc.contributor.author
Szabó, Tibor
dc.date.accessioned
2021-05-10T09:38:49Z
dc.date.available
2021-05-10T09:38:49Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/30705
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-30444
dc.description.abstract
Two n×n Latin squares L1,L2 are said to be orthogonal if, for every ordered pair (x, y) of symbols, there are coordinates (i, j) such that L1(i,j)=x and L2(i,j)=y. A k-MOLS is a sequence of k pairwise-orthogonal Latin squares, and the existence and enumeration of these objects has attracted a great deal of attention. Recent work of Keevash and Luria provides, for all fixed k, log-asymptotically tight bounds on the number of k-MOLS. To study the situation when k grows with n, we bound the number of ways a k-MOLS can be extended to a (k+1)-MOLS. These bounds are again tight for constant k, and allow us to deduce upper bounds on the total number of k-MOLS for all k. These bounds are close to tight even for k linear in n, and readily generalise to the broader class of gerechte designs, which include Sudoku squares.
en
dc.format.extent
20 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Latin squares
en
dc.subject
Orthogonal mates
en
dc.subject
Gerechte designs
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Enumerating extensions of mutually orthogonal Latin squares
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.1007/s10623-020-00771-6
dcterms.bibliographicCitation.journaltitle
Designs, Codes and Cryptography
dcterms.bibliographicCitation.number
10
dcterms.bibliographicCitation.pagestart
2187
dcterms.bibliographicCitation.pageend
2206
dcterms.bibliographicCitation.volume
88
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s10623-020-00771-6
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
![Dieser Normdateneintrag wurde von einer Benutzerin oder einem Benutzer als gültig bestätigt.](/cache_202e45ad85b55efaeb29160f63cd3f3b/themes/FuCD/images/authority_control/invisible.gif)
refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.issn
0925-1022
dcterms.isPartOf.eissn
1573-7586