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 equivalent to 3,19 (mod 48).
3-pyramidal Steiner triple systems / Buratti, Marco; Rinaldi, Gloria; Traetta, Tommaso. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3966. - 13:1(2017), pp. 95-106. [10.26493/1855-3974.998.38f]
3-pyramidal Steiner triple systems
Buratti, Marco;
2017
Abstract
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 equivalent to 3,19 (mod 48).| File | Dimensione | Formato | |
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