General frame constructions for Z-cyclic triplewhist tournaments

Authors:
Gennian Ge
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 18
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Abstract

Frames are useful in dealing with resolvable designs such as resolvable balanced incomplete block designs and triplewhist tournaments. Z-cyclic triplewhist tournament frames are also useful in the constructions of Z-cyclic triplewhist tournaments. In this paper, the concept of an (h"1,h"2,...,h"n;u)-regular Z-cyclic triplewhist tournament frame is defined, and used to establish several quite general recursive constructions for Z-cyclic triplewhist tournaments. As corollaries, we are able to unify many known constructions for Z-cyclic triplewhist tournaments. As an application, some new Z-cyclic triplewhist tournament frames and Z-cyclic triplewhist tournaments are obtained. The known existence results of such designs are then extended.