3-pyramidal Steiner triple systems

Marco Buratti, Gloria Rinaldi, Tommaso Traetta


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).


Steiner triple system, group action, difference family, Skolem sequence, Langford sequence

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ISSN: 1855-3974

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