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

Mark Pankov

paper

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

arXiv:2508.16963

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.

Symmetric (2k−1,2k−1,2k−2)-designs which are (2k−1−1)-pyramidal over abelian groups

Abstract

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