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Contribution

Some bounds on the number of cyclic Steiner 2-designs

Speakers

  • Dr. Emanuele BRUGNOLI

Primary authors

Content

A $2-(v,k,1)$ design or, also, a Steiner $2$-design is said to be cyclic if it admits an automorphism cyclically permuting all its points. To establish the number NC$(v,k)$ of cyclic $2-(v,k,1)$ designs is in general not feasible and very little is known about this number. By ``playing'' with $(v,k,1)$ difference families, some lower bounds on NC$(v,k)$ are given. In particular, for primes $p=6n+1$ with $p\equiv\pm 1$ (mod $5$), a construction involving the golden ratio of $\mathbb{Z}_p$ and the Narayana cows sequence is shown to give NC$(p,3)>2^{3n/2}$.