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Avoiding multiple entry arrays.

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Avoiding multiple entry arrays. / Chetwynd, Amanda G.; Rhodes, S. J.
In: Journal of Graph Theory, Vol. 25, No. 4, 08.1997, p. 257-266.

Research output: Contribution to Journal/MagazineJournal article

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Chetwynd AG, Rhodes SJ. Avoiding multiple entry arrays. Journal of Graph Theory. 1997 Aug;25(4):257-266. doi: 10.1002/(SICI)1097-0118(199708)25:4<257::AID-JGT3>3.0.CO;2-J

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Chetwynd, Amanda G. ; Rhodes, S. J. / Avoiding multiple entry arrays. In: Journal of Graph Theory. 1997 ; Vol. 25, No. 4. pp. 257-266.

Bibtex

@article{3c87e5dbeb4749209631c630469c98c4,
title = "Avoiding multiple entry arrays.",
abstract = "In this paper we consider the problem of avoiding arrays with more than one entry per cell. An n × n array on n symbols is said to be if an n × n latin square, on the same symbols, can be found which differs from the array in every cell. Our first result is for chessboard squares with at most two entries per black cell. We show that if k 1 and C is a 4k × 4k chessboard square on symbols 1, 2, , 4k in which every black cell contains at most two symbols and every symbol appears at most once in every row and column, then C is avoidable. Our main result is for squares with at most two entries in any cell and answers a question of Hilton. If k 3240 and F is a 4k × 4k array on 1, 2,, 4k in which every cell contains at most two symbols and every symbol appears at most twice in every row and column, then F is avoidable",
keywords = "latin • squares • restricted • colourings",
author = "Chetwynd, {Amanda G.} and Rhodes, {S. J.}",
year = "1997",
month = aug,
doi = "10.1002/(SICI)1097-0118(199708)25:4<257::AID-JGT3>3.0.CO;2-J",
language = "English",
volume = "25",
pages = "257--266",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "4",

}

RIS

TY - JOUR

T1 - Avoiding multiple entry arrays.

AU - Chetwynd, Amanda G.

AU - Rhodes, S. J.

PY - 1997/8

Y1 - 1997/8

N2 - In this paper we consider the problem of avoiding arrays with more than one entry per cell. An n × n array on n symbols is said to be if an n × n latin square, on the same symbols, can be found which differs from the array in every cell. Our first result is for chessboard squares with at most two entries per black cell. We show that if k 1 and C is a 4k × 4k chessboard square on symbols 1, 2, , 4k in which every black cell contains at most two symbols and every symbol appears at most once in every row and column, then C is avoidable. Our main result is for squares with at most two entries in any cell and answers a question of Hilton. If k 3240 and F is a 4k × 4k array on 1, 2,, 4k in which every cell contains at most two symbols and every symbol appears at most twice in every row and column, then F is avoidable

AB - In this paper we consider the problem of avoiding arrays with more than one entry per cell. An n × n array on n symbols is said to be if an n × n latin square, on the same symbols, can be found which differs from the array in every cell. Our first result is for chessboard squares with at most two entries per black cell. We show that if k 1 and C is a 4k × 4k chessboard square on symbols 1, 2, , 4k in which every black cell contains at most two symbols and every symbol appears at most once in every row and column, then C is avoidable. Our main result is for squares with at most two entries in any cell and answers a question of Hilton. If k 3240 and F is a 4k × 4k array on 1, 2,, 4k in which every cell contains at most two symbols and every symbol appears at most twice in every row and column, then F is avoidable

KW - latin • squares • restricted • colourings

U2 - 10.1002/(SICI)1097-0118(199708)25:4<257::AID-JGT3>3.0.CO;2-J

DO - 10.1002/(SICI)1097-0118(199708)25:4<257::AID-JGT3>3.0.CO;2-J

M3 - Journal article

VL - 25

SP - 257

EP - 266

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 4

ER -