Further Results on Large Sets of Resolvable Idempotent Latin Squares | Zendy

Zhou Junling | Zendy; Chang Yanxun | Zendy

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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 } .

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