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Restricted completion of sparse partial Latin squares
Malardalen Univ, Sweden; Mittag Leffler Inst, Sweden.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. Mittag Leffler Inst, Sweden.
Umea Univ, Sweden; Mittag Leffler Inst, Sweden.
2019 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 28, no 5, p. 675-695Article in journal (Refereed) Published
##### Abstract [en]

An n x n Martial Latin square P is called dense if each row and column has at mostan non-empty cells and each symboloccurso n times in P. An x n arrayA where each cell contains subset of {1, ..., n} is a (beta n, beta n, beta n)-array if each symbol occurs at most beta n times in each row and column and each cell contains a set of size at most beta n. Combining the notions of completing partial Latin squared and avoiding arrays, we prose that there are constants alpha, beta amp;gt; 0 such that, for every positive integer n, if P is an alpha-dense n x n partial a square, A is an n x n (beta n, beta n, beta n)-array and no cell of P contains a symbol that ppears in the corresponing cell of A, then there is a completiong of P that avoids A; that is, there is a Latin square L that agrees with P on every non-empty of P, and for each i, j satisfying 1 amp;lt;= i, j, amp;lt;= n, the symbol in position (i, j) in L does not appear in the corresponding cell of A.

##### Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2019. Vol. 28, no 5, p. 675-695
##### National Category
Discrete Mathematics
##### Identifiers
ISI: 000500255000002OAI: oai:DiVA.org:liu-162770DiVA, id: diva2:1379756
##### Note

Funding Agencies|Mittag-Leffler Institute

Available from: 2019-12-17 Created: 2019-12-17 Last updated: 2020-03-11

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Casselgren, Carl Johan
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Mathematics and Applied MathematicsFaculty of Science & Engineering
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