常彦勋,雷建国
CHANG Pan-Xun, LEI Jian-Guo
摘要：
A idempotent quasigroup (Q, ?) of order n is equivalent to an n(n − 1) × 3
partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a
(n + 1)-set. Denote by T(n + 1) the set of (n + 1)n(n − 1) ordered triples of X with the
property that the 3 coordinates of each ordered triple are distinct. An overlarge set of
idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n−1)×3 partial
orthogonal arrays Ax, x ∈ X based on X \ {x}. This article gives an almost complete
solution of overlarge sets of idempotent quasigroups.
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