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Enumerating Steiner triple systems
Journal of Combinatorial Designs, 2023 AbstractSteiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes.
Östergård +2 more
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Bicoloring Steiner Triple Systems [PDF]
The Electronic Journal of Combinatorics, 1999 A Steiner triple system has a bicoloring with $m$ color classes if the points are partitioned into $m$ subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give a multiplication theorem for Steiner triple ...
Colbourn, Charles J. +2 more
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Sequencing partial Steiner triple systems [PDF]
Journal of Combinatorial Designs, 2019 AbstractA partial Steiner triple system of order is sequenceable if there is a sequence of length of its distinct points such that no proper segment of the sequence is a union of point‐disjoint blocks. We prove that if a partial Steiner triple system has at most three point‐disjoint blocks, then it is sequenceable.
Brian Alspach +2 more
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Simple Signed Steiner Triple Systems [PDF]
Journal of Combinatorial Designs, 2012 AbstractLetXbe av‐set,be a set of 3‐subsets (triples) ofX, andbe a partition ofwith. The pairis called a simple signed Steiner triple system, denoted by ST, if the number of occurrences of every 2‐subset ofXin triplesis one more than the number of occurrences in triples. In this paper, we prove thatexists if and only if,, and, whereand for,.
Ghorbani, E., Khosrovshahi, G. B.
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Unbalanced steiner triple systems
Journal of Combinatorial Theory, Series A, 1994 The authors study colouring properties of Steiner triple systems and derive several inequalities for sizes of their colour classes. Answering a question of A. Rosa, they give a construction (for any \(l\geq 6\)) of a family of \(l\)-chromatic Steiner triple systems with the following remarkable property: No matter how they are \(l\)-coloured, almost ...
Haddad, Lucien, Rödl, Vojtech
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Balanced Steiner Triple Systems
Journal of Combinatorial Theory, Series A, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Colbourn, Charles +2 more
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3-pyramidal Steiner triple systems
Ars Mathematica Contemporanea, 2017 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 ...
Buratti, Marco +2 more
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Steiner Triple Systems without Parallel Classes [PDF]
SIAM Journal on Discrete Mathematics, 2015 5 pages, 0 figures. This version fixes a minor error in the journal version of the paper where we had neglected to say that two sum-zero triples must be removed before the additional triples in $\mathcal{B}^\infty \cup \mathcal{B}^*$ are added to create the Steiner triple ...
Bryant, Darryn, Horsley, Daniel
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Bicyclic Steiner triple systems
Discrete Mathematics, 1994 A permutation \(\pi\) of a \(v\)-element set is said to be of type \([\pi]=[p_ 1,p_ 2,\ldots,p_ v]\) if the disjoint cyclic decomposition of \(\pi\) contains \(p_ i\) cycles of length \(i\). Thus a cyclic Steiner triple system STS\((v)\) is one admitting an automorphism of type \([0,0,\ldots,0,1]\). A bicyclic Steiner triple system is defined to be one
Calahan-Zijlstra, Rebecca +1 more
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Further 6-sparse Steiner Triple Systems [PDF]
Graphs and Combinatorics, 2009 Erdös conjectured that for each \(k\geq 4\) there exists \(v(k)\) so that for every admissible \(v>v(k)\) there exists a Steiner Triple System on \(v\) points, \(STS(v),\) which does contains no configuration having \(n\) blocks on \(n+2\) points for \(n\) with \(4\leq n\leq k.\) Such \(STS(v)\) is called to be \(k\)-sparse.
Forbes, A. D. +2 more
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