Abstract
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.
Original language | English |
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Pages (from-to) | 93-105 |
Number of pages | 13 |
Journal | Designs, Codes, and Cryptography |
Volume | 52 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jul 2009 |
Externally published | Yes |