Nonextendible Latin cuboids

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

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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 languageEnglish
Pages (from-to)239 - 249
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume26
Issue number1
DOIs
Publication statusPublished - 2012

Cite this

Bryant, D. E., Cavenagh, N., Maenhaut, B. M., Pula, K., & Wanless, I. M. (2012). Nonextendible Latin cuboids. SIAM Journal on Discrete Mathematics, 26(1), 239 - 249. https://doi.org/10.1137/110825534