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arXiv · 1603.09645

$3$-pyramidal Steiner Triple Systems

Marco Buratti·Gloria Rinaldi·Tommaso Traetta
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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 $v\equiv7,9,15$ (mod $24$) or $v\equiv 3, 19$ (mod 48).

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Marco Buratti, Gloria Rinaldi, Tommaso Traetta. 2016-03-31. $3$-pyramidal Steiner Triple Systems. https://arxiv.org/abs/1603.09645

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