2016/03/31 by Buratti, Marco, Rinaldi, Gloria, Traetta, Tommaso
#05B07 #Combinatorics (math.CO) #FOS: Mathematics #G.2.0
paper · doi:10.48550/arxiv.1603.09645
A design is said to be f-pyramidal when it has an automorphism group which fixes f points and acts sharply transitively on all the others. The problem of establishing the set of values of v for which there exists an f-pyramidal Steiner triple system of order v has been deeply investigated in the case f=1 but it remains open for a special class of values of v. The same problem for the next possible f, which is f=3, is here completely solved: there exists a 3-pyramidal Steiner triple system of order v if and only if v≡7,9,15 (mod 24) or v≡ 3, 19 (mod 48).