Computer Search for Large Sets of Idempotent Quasigroups

Authors:
Feifei Ma;Jian Zhang
Affiliations:
State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences, and Chinese Academy of Sciences, Graduate University,;State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences,
Venue:
Computer Mathematics
Year:
2008

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Abstract

A collection of n茂戮驴 2 idempotent quasigroups of order nis 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).