P3BD‐closed sets | Zendy

Zhou Junling | Zendy; Chang Yanxun | Zendy

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P3BD‐closed sets

Author(s) -

Zhou Junling,

Chang Yanxun

Publication year - 2011

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.20292

Subject(s) - idempotence , mathematics , closure (psychology) , combinatorics , set (abstract data type) , closed set , discrete mathematics , computer science , law , political science , programming language

A concept called P3BD‐closed set is introduced to describe a set of positive integers which is both PBD‐closed and 3BD‐closed. The theory of P3BD‐closure is developed and a few examples of P3BD‐closed sets are exhibited. In the process, the existence spectrum of OLIQ ⋄ s (overlarge sets of idempotent quasigroups with their own idempotent orthogonal mates) is almost determined. A pair of orthogonal OLIQ ⋄ s is shown to asymptotically exist. The existence of OLIQ s (overlarge sets of idempotent quasigroups with their own orthogonal mates not necessarily specifying idempotency) is also established with only 10 possible exceptions remained. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:407‐421, 2011

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