Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 4: 717 - 726

DOI: https://doi.org/10.1007/s11464-010-0069-6

RESEARCH ARTICLE

Spectrum of resolvable directed quadruple systems

  • Jian WANG 1 ,
  • Beiliang DU , 2
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  • 1. Nantong Vocational College, Nantong 226007, China
  • 2. Department of Mathematics, Suzhou University, Suzhou 215006, China

Received date: 07 Nov 2009

Accepted date: 02 Jun 2010

Published date: 05 Dec 2010

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

A t-(v, k, 1) directed design (or simply a t-(v, k, 1)DD) is a pair (S, ), where S is a v-set and is a collection of k-tuples (called blocks) of S, such that every t-tuple of S belongs to a unique block. The t-(v, k, 1)DD is called resolvable if can be partitioned into some parallel classes, so that each parallel class is a partition of S. It is proved that a resolvable 3-(v, 4, 1)DD exists if and only if v ≡ 0 (mod 4).

Key words： n-tuple; directed design; resolvable directed quadruple system

Cite this article

Jian WANG , Beiliang DU . Spectrum of resolvable directed quadruple systems[J]. Frontiers of Mathematics in China, 2010 , 5(4) : 717 -726 . DOI: 10.1007/s11464-010-0069-6

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