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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Computer Search for Large Sets of Idempotent Quasigroups
verfasst von : Feifei Ma, Jian Zhang
Erschienen in: Computer Mathematics
Verlag: Springer Berlin Heidelberg
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A collection of
n
− 2 idempotent quasigroups of order
n
is called a large set if any two of them are disjoint, denoted by
LIQ
(
n
). While the existence of ordinary
LIQ
(
n
) has been extensively studied, the spectrums of large sets of idempotent quasigroups with various identities remain open, for example, large set of Steiner pentagon quasigroups of order 11 which is denoted by
LSPQ
(11). This paper describes some computer searching efforts seeking to solve such problems. A series of results are obtained, including the non-existence of
LSPQ
(11).