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$3$-pyramidal Steiner Triple Systems | | Marco Buratti
; Gloria Rinaldi
; Tommaso Traetta
; | | Date: |
31 Mar 2016 | | 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 $vequiv7,9,15$ (mod $24$) or $vequiv 3, 19$ (mod 48). | | Source: | arXiv, 1603.9645 | | Services: | Forum | Review | PDF | Favorites | |
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