TY - JOUR

T1 - Indivisible plexes in latin squares

AU - Bryant, Darryn Edward

AU - Egan, Judith Ann

AU - Maenhaut, Barbara Marguerite

AU - Wanless, Ian Murray

PY - 2009

Y1 - 2009

N2 - 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 = 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.

AB - 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 = 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.

UR - http://apps.isiknowledge.com.ezproxy.lib.monash.edu.au/full_record.do?product=UA&search_mode=GeneralSearch&qid=2&SID=U1IgmPHi3pjn4G4kjef&page=1&doc=1&

M3 - Article

SN - 0925-1022

VL - 52

SP - 93

EP - 105

JO - Designs Codes and Cryptography

JF - Designs Codes and Cryptography

IS - 1

ER -