Disjoint Subquasigroups | Zendy

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Disjoint Subquasigroups

Author(s) -

Heinrich Katherine

Publication year - 1982

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-45.3.547

Subject(s) - mathematics , disjoint sets , combinatorics , order (exchange) , existential quantification , latin square , discrete mathematics , rumen , chemistry , food science , finance , fermentation , economics

Denote by RP(a, b; s, t ), with a < b , a latin square of order n = as + bt with s disjoint subsquares of order a and t of order b . We show that RP(a, b; s, t ) exists for all s ⩾ 3, t ⩾ 3, that RP(a, b ; 1, t ) exists if and only if t ⩾ 3, that RP(a, b; s ,1) exists if and only if s ⩾ 3 and ( s — 1) a ⩾ b , and that there exist integers T = T(a,b and S = S(a, b ) such that for all t ⩾ T and s ⩾ S, RP(a, b ;2, t ) and RP(a, b; s , 2) exist.

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