# Indivisible plexes in latin squares

Bryant, D., Egan, J., Maenhaut, B. and Wanless, I. M. (2009) Indivisible plexes in latin squares. Designs, Codes and Cryptography, 52 1: 93-105. doi:10.1007/s10623-009-9269-z

Author Bryant, D.Egan, J.Maenhaut, B.Wanless, I. M. Indivisible plexes in latin squares Designs, Codes and Cryptography   Check publisher's open access policy 0925-1022 2009-07-01 2009 Article (original research) 10.1007/s10623-009-9269-z Not yet assessed 52 1 93 105 13 D. JungnickelJ. D. KeyP. Wild United States Springer eng C1970101 Expanding Knowledge in the Mathematical Sciences010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) A k-plex is a selection of kn entries of a latin square of order n in which each row, column and symbol is represented precisely k times. A transversal of a latin square corresponds to the case k = 1. A k-plex is said to be indivisible if it contains no c-plex for any 0 < c < k. We prove that if n = 2km for integers k >= 2 and m >= 1 then there exists a latin square of order n composed of 2m disjoint indivisible k-plexes. Also, for positive integers k and n satisfying n = 3k, n = 4k or n >= 5k, we construct a latin square of order n containing an indivisible k-plex. A k-plex is a selection of kn entries of a latin square of order n in which each row, column and symbol is represented precisely k times. A transversal of a latin square corresponds to the case k = 1. A k-plex is said to be indivisible if it contains no c-plex for any 0 < c < k. We prove that if n = 2km for integers k ≥ 2 and m ≥ 1 then there exists a latin square of order n composed of 2m disjoint indivisible k-plexes. Also, for positive integers k and n satisfying n = 3k, n = 4k or n ≥ 5k, we construct a latin square of order n containing an indivisible k-plex. Latin squareTransversalPlexOrthogonal partition C1 Confirmed Code UQ

 Document type: Journal Article Article (original research) School of Mathematics and Physics 2010 Higher Education Research Data Collection

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