A design is said to be f-pyramidal when it admits an automorphism group fixing f points and acting sharply transitiveky on all the others. The problem of establishing the set of values of v for which there exists a f-pyramidal Steiner system of order v was deeply investigated in the case f=1 but it remains open for special classes of v. The same problem for the next class of f, which is f=3, is completly solved here. 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).

3-pyramidal Steiner triple systems / Buratti, Marco; Rinaldi, Gloria; Traetta, Tommaso. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3974. - STAMPA. - 13:1(2017), pp. 95-106. [10.26493/1855-3974.998.38f]

3-pyramidal Steiner triple systems

RINALDI, Gloria;
2017

Abstract

A design is said to be f-pyramidal when it admits an automorphism group fixing f points and acting sharply transitiveky on all the others. The problem of establishing the set of values of v for which there exists a f-pyramidal Steiner system of order v was deeply investigated in the case f=1 but it remains open for special classes of v. The same problem for the next class of f, which is f=3, is completly solved here. 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).
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3-pyramidal Steiner triple systems / Buratti, Marco; Rinaldi, Gloria; Traetta, Tommaso. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3974. - STAMPA. - 13:1(2017), pp. 95-106. [10.26493/1855-3974.998.38f]
Buratti, Marco; Rinaldi, Gloria; Traetta, Tommaso
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1129296
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