Super-simple, pan-orientable and pan-decomposable GDDs with block size 4
| Autor: | R. J. R. Abel, Frank E. Bennett |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Discrete mathematics
BIBD Super-simple Block (permutation group theory) Complete graph 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Type (model theory) 01 natural sciences Spectrum (topology) Theoretical Computer Science Combinatorics 010201 computation theory & mathematics Simple (abstract algebra) Pan-orientable k-tournament 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics GDD Pan-decomposable k-tournament Block size Graphs and Combinatorics Mathematics |
| Zdroj: | Discrete Mathematics. 310:1066-1079 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2009.11.001 |
| Popis: | In this paper we study (4,[email protected])-GDDs of type g^n possessing both the pan-decomposable property introduced by Granville, Moisiadis, Rees, On complementary decompositions of the complete graph, Graphs and Combinatorics 5 (1989) 57-61 and the pan-orientable property introduced by Gruttmuller, Hartmann, Pan-orientable block designs, Australas. J. Combin. 40 (2008) 57-68. We show that the necessary condition for a (4,[email protected])-GDD satisfying both of these properties, namely (1) n>=4, @mg(n-1)=0 (mod 3), and (2) g-1,n are not both even if @m is odd are sufficient. When @l=2, our designs are super-simple. We also determine the spectrum of (4,2)-GDDs which are super-simple and possess some of the decomposable/orientable conditions, but are not pan-decomposable or pan-orientable. In particular, we show that the necessary conditions for a super-simple directable (4,2)-GDD of type g^n are sufficient. |
| Databáze: | OpenAIRE |
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