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

2025/08/23 by Pankov, Mark
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/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.

Citations

• The existence of pyramidal Steiner triple systems over abelian groups
• Symmetric (15,8,4)-designs in terms of the geometry of binary simplex codes of dimension 4
• Point-line geometries related to binary equidistant codes
• A combinatorial proof of Fisher's Inequality

Related

• Flag-transitive symmetric 2-designs]The symmetric 2-(v,k,λ) designs, with k>λ(λ-3 )/2, admitting a flag-transitive, point imprimitive automorphism group are known
• Classification of the non-trivial 2-(k²,k,λ) designs, with λ| k, admitting a flag-transitive almost simple automorphism group
• A classification of flag-transitive block designs
• Pairwise transitive 2-designs
• New symmetric 2-(176,50,14) designs