Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences

Details Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences

2010-08-10

arxiv.org/abs/1008.1608v1

Mathematics

Combinatorics

18 pages, to appear in Mathematics of Computation

Scientific paper

A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. Application to the construction of short 2-radius sequences is given, with some new 2-radius sequences found through computer search.

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