Premium
Further Results on Large Sets of Resolvable Idempotent Latin Squares
Author(s) -
Zhou Junling,
Chang Yanxun
Publication year - 2012
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21305
Subject(s) - mathematics , latin square , combinatorics , diagonal , idempotence , disjoint sets , order (exchange) , integer (computer science) , pairwise comparison , discrete mathematics , statistics , geometry , rumen , chemistry , food science , finance , fermentation , computer science , economics , programming language
An idempotent Latin square of order v is called resolvable and denoted by RILS( v ) if the v ( v − 1 ) off‐diagonal cells can be resolved into v − 1 disjoint transversals. A large set of resolvable idempotent Latin squares of order v , briefly LRILS( v ), is a collection of v − 2 RILS( v )s pairwise agreeing on only the main diagonal. In this paper, it is established that there exists an LRILS( v ) for any positive integer v ≥ 3 , except for v = 6 , and except possibly for v ∈ { 14 , 20 , 22 , 26 , 28 , 34 , 35 , 38 , 40 , 42 , 46 , 50 , 55 , 62 } .