English

The existence of cyclic (v,4,1)-designs

Combinatorics 2022-07-05 v2

Abstract

Even though Peltesohn proved that a cyclic (v,3,1)-design exists if and only if v1,3(mod6)v\equiv 1,3\pmod{6} as early as 1939, the problem of determining the spectrum of cyclic (v,k,1)-designs with k>3 is far from being settled, even for k=4. This paper shows that a cyclic (v,4,1)-design exists if and only if v1,4(mod12)v\equiv 1,4\pmod{12} and v∉{16,25,28}v\not\in\{16,25,28\}.

Keywords

Cite

@article{arxiv.2206.06751,
  title  = {The existence of cyclic (v,4,1)-designs},
  author = {Menglong Zhang and Tao Feng and Xiaomiao Wang},
  journal= {arXiv preprint arXiv:2206.06751},
  year   = {2022}
}