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Spectrum of resolvable directed quadruple systems |
Jian WANG1, Beiliang DU2( ) |
| 1. Nantong Vocational College, Nantong 226007, China; 2. Department of Mathematics, Suzhou University, Suzhou 215006, China |
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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).
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| Keywords
n-tuple
directed design
resolvable directed quadruple system
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Corresponding Author(s):
DU Beiliang,Email:dubl@suda.edu.cn
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Issue Date: 05 December 2010
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