Symmetric $(2^k-1,2^{k-1},2^{k-2})$-designs which are $(2^{k-1}-1)$-pyramidal over abelian groups

Mark Pankov

Symmetric $(2^k-1,2^{k-1},2^{k-2})$-designs which are $(2^{k-1}-1)$-pyramidal over abelian groups

Combinatorics 2025-08-26 v1

Authors: Mark Pankov

Abstract

A design is called $t$ -pyramidal when it has an automorphism group which fixes $t$ points and acts sharply transitively on the remaining points. We determine all symmetric $(2^k-1,2^{k-1},2^{k-2})$ -designs which are $(2^{k-1}-1)$ -pyramidal over abelian groups.

Keywords

design theory symmetric designs pyramidal designs automorphism group abelian groups

Cite

@article{arxiv.2508.16963,
  title  = {Symmetric $(2^k-1,2^{k-1},2^{k-2})$-designs which are $(2^{k-1}-1)$-pyramidal over abelian groups},
  author = {Mark Pankov},
  journal= {arXiv preprint arXiv:2508.16963},
  year   = {2025}
}

Related papers

View all related →