Nonextendible Latin cuboids

Darryn Edward Bryant; Nicholas Cavenagh; Barbara Marguerite Maenhaut; Kyle Pula; Ian Murray Wanless

doi:10.1137/110825534

Nonextendible Latin cuboids

Darryn Edward Bryant, Nicholas Cavenagh, Barbara Marguerite Maenhaut, Kyle Pula, Ian Murray Wanless

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

We show that for all integers m >= 4 there exists a 2m x 2m x m latin cuboid that cannot be completed to a 2mx2mx2m latin cube. We also show that for all even m > 2 there exists a (2m-1) x (2m-1) x (m-1) latin cuboid that cannot be extended to any (2m-1) x (2m-1) x m latin cuboid.

Original language	English
Pages (from-to)	239 - 249
Number of pages	11
Journal	SIAM Journal on Discrete Mathematics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1137/110825534
Publication status	Published - 2012

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10.1137/110825534

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Cite this

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title = "Nonextendible Latin cuboids",

abstract = "We show that for all integers m >= 4 there exists a 2m x 2m x m latin cuboid that cannot be completed to a 2mx2mx2m latin cube. We also show that for all even m > 2 there exists a (2m-1) x (2m-1) x (m-1) latin cuboid that cannot be extended to any (2m-1) x (2m-1) x m latin cuboid.",

author = "Bryant, {Darryn Edward} and Nicholas Cavenagh and Maenhaut, {Barbara Marguerite} and Kyle Pula and Wanless, {Ian Murray}",

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language = "English",

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publisher = "Society for Industrial & Applied Mathematics (SIAM)",

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AU - Cavenagh, Nicholas

AU - Maenhaut, Barbara Marguerite

AU - Pula, Kyle

AU - Wanless, Ian Murray

PY - 2012

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AB - We show that for all integers m >= 4 there exists a 2m x 2m x m latin cuboid that cannot be completed to a 2mx2mx2m latin cube. We also show that for all even m > 2 there exists a (2m-1) x (2m-1) x (m-1) latin cuboid that cannot be extended to any (2m-1) x (2m-1) x m latin cuboid.

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U2 - 10.1137/110825534

DO - 10.1137/110825534

M3 - Article

VL - 26

SP - 239

EP - 249

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 1

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