Year: 2025
Type: article
Abstract: A Steiner triple system STS( v ) is called f -pyramidal if it has an automorphism group fixing f points and acting sharply transitively on the remaining $$v-f$$ v - f points. In this paper, we focus on the STSs that are f -pyramidal over some abelian group. Their existence has been settled only for the smallest admissible values of f , that is, $$f=0,1,3$$ f = 0 , 1 , 3 . In this paper, we complete this result and determine, for every $$f>3$$ f > 3 , the spectrum of values ( f , v ) for which there is an f -pyramidal STS( v ) over an abelian group. This result is obtained by constructing difference families relative to a suitable partial spread.
Source: Designs Codes and Cryptography
Authors: Yanxun Chang, Tommaso Traetta, Junling Zhou
Institutions: Beijing Jiaotong University, University of Brescia
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4414577486