2012/04/14 by Victoria Horan, Horan, Victoria, Glenn Hurlbert +1
Computer Science · Engineering · Mathematics · #68R15 (Primary) 05B05 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1204.3215
openalex publication_date 2012/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is will known that Steiner quadruple systems of order v, or SQS(v), exist if and only if v = 2, 4 mod 6. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole. Using Hanani's SQS constructions, we show that for every v = 2, 4 mod 6 with v > 4 there exists an SQS(v) that admits a 1-overlap cycle.