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Partial latin squares are avoidable
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 15, no 3, 485-497 p.Article in journal (Refereed) Published
Abstract [en]

A square array is avoidable if for each set of n symbols there is an n x n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m >= 2 any partial Latin square of order 4m - 1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable.

Place, publisher, year, edition, pages
2011. Vol. 15, no 3, 485-497 p.
Keyword [en]
Latin square, partial Latin square, avoidable array
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-5317DOI: 10.1007/s00026-011-0106-5OAI: oai:DiVA.org:umu-5317DiVA: diva2:144798
Available from: 2006-09-15 Created: 2006-09-15 Last updated: 2017-12-14Bibliographically approved
In thesis
1. How to do what you want to do when you can not do what you want: on avoiding and completing partial latin squares
Open this publication in new window or tab >>How to do what you want to do when you can not do what you want: on avoiding and completing partial latin squares
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Matematik och matematisk statistik, 2006. 9 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 1102-8300
Keyword
Latin squares, constraint satisfaction, schedulling, array,
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-867 (URN)91-7264-143-6 (ISBN)
Public defence
2006-10-06, MA 121, MIT-huset, Umeå universitet, Umeå, 10:15
Opponent
Supervisors
Available from: 2006-09-15 Created: 2006-09-15Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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