Spectrum of resolvable directed quadruple systems

Abstract

A t-(v, k, 1) directed design (or simply a t-(v, k, 1)DD) is a pair (S, ℐ), where S is a v-set and ℐ 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 ℐ 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).

Keywords

n-tuple / directed design / resolvable directed quadruple system

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