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Avoiding Arrays of ...
Avoiding Arrays of Odd Order by Latin Squares
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- Andren, Lina J. (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Sweden
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- Casselgren, Carl Johan (författare)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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- Öhman, Lars-Daniel (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Sweden
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(creator_code:org_t)
- Cambridge University Press (CUP), 2013
- 2013
- Engelska.
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Ingår i: Combinatorics, probability & computing. - : Cambridge University Press (CUP). - 0963-5483 .- 1469-2163. ; 22:2, s. 184-212
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m andlt;= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -andgt; infinity.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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