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Avoiding partial Latin squares and intricacy.

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Avoiding partial Latin squares and intricacy. / Chetwynd, Amanda G.; Rhodes, Susan J.
In: Discrete Mathematics, Vol. 177, No. 1-3, 01.12.1997, p. 17-32.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Chetwynd, AG & Rhodes, SJ 1997, 'Avoiding partial Latin squares and intricacy.', Discrete Mathematics, vol. 177, no. 1-3, pp. 17-32. https://doi.org/10.1016/S0012-365X(96)00354-8

APA

Chetwynd, A. G., & Rhodes, S. J. (1997). Avoiding partial Latin squares and intricacy. Discrete Mathematics, 177(1-3), 17-32. https://doi.org/10.1016/S0012-365X(96)00354-8

Vancouver

Chetwynd AG, Rhodes SJ. Avoiding partial Latin squares and intricacy. Discrete Mathematics. 1997 Dec 1;177(1-3):17-32. doi: 10.1016/S0012-365X(96)00354-8

Author

Chetwynd, Amanda G. ; Rhodes, Susan J. / Avoiding partial Latin squares and intricacy. In: Discrete Mathematics. 1997 ; Vol. 177, No. 1-3. pp. 17-32.

Bibtex

@article{539df314b869448087c75a14d8ac80b7,
title = "Avoiding partial Latin squares and intricacy.",
abstract = "In this paper we consider the following problem: Given a partial n × n latin square P on symbols 1, 2,…, n, is it possible to find an n × n latin square L on the same symbols which differs from P in every cell? In other words, is P avoidable? We show that all 2k × 2k partial latin squares for k 2 are avoidable and give some results on odd partial latin squares. We also use these results to show that the intricacy of avoiding partial latin squares is two and of avoiding more general arrays is at most three.",
author = "Chetwynd, {Amanda G.} and Rhodes, {Susan J.}",
year = "1997",
month = dec,
day = "1",
doi = "10.1016/S0012-365X(96)00354-8",
language = "English",
volume = "177",
pages = "17--32",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

RIS

TY - JOUR

T1 - Avoiding partial Latin squares and intricacy.

AU - Chetwynd, Amanda G.

AU - Rhodes, Susan J.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - In this paper we consider the following problem: Given a partial n × n latin square P on symbols 1, 2,…, n, is it possible to find an n × n latin square L on the same symbols which differs from P in every cell? In other words, is P avoidable? We show that all 2k × 2k partial latin squares for k 2 are avoidable and give some results on odd partial latin squares. We also use these results to show that the intricacy of avoiding partial latin squares is two and of avoiding more general arrays is at most three.

AB - In this paper we consider the following problem: Given a partial n × n latin square P on symbols 1, 2,…, n, is it possible to find an n × n latin square L on the same symbols which differs from P in every cell? In other words, is P avoidable? We show that all 2k × 2k partial latin squares for k 2 are avoidable and give some results on odd partial latin squares. We also use these results to show that the intricacy of avoiding partial latin squares is two and of avoiding more general arrays is at most three.

U2 - 10.1016/S0012-365X(96)00354-8

DO - 10.1016/S0012-365X(96)00354-8

M3 - Journal article

VL - 177

SP - 17

EP - 32

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -