Results 21 to 30 of about 2,403 (227)

Equitable embeddings of steiner triple systems

Journal of Combinatorial Theory, Series A, 1996
An \(n\)-colouring of a Steiner triple system \(\text{STS}(v)\) is a map which assigns one colour, from a set of \(n\) given colours, to each point in such a way that no triple is monochromatic. An STS is \(r\)-chromatic if it can be \(r\)-coloured but not \((r- 1)\)-coloured.
Charles J. Colbourn, Lucien Haddad, Václav Linek   +2 more
openaire   +2 more sources

Twin Steiner triple systems

Discrete Mathematics, 1997
A set of blocks of the form \(\{a,x,y\}, \{a,z,w\}, \{b,x,w\}, \{b,z,y\}\) in a Steiner triple system STS\((v)\) is called a Pasch configuration. Replacing these blocks by \(\{b,x,y\}, \{b,z,w\}, \{a,x,w\}, \{a,z,y\}\) produces a new STS\((v)\), which may or may not be isomorphic to the original design. This paper contributes to an investigation of the
Mike J. Grannell, Terry S. Griggs, J. P. Murphy   +2 more
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Identical twin Steiner triple systems [PDF]

Australas. J Comb., 2016
Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33.
Grannell, M. J., Lovegrove, G. J.
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Automorphism groups of Steiner triple systems [PDF]

, 2022
If G is a finite group then there is an integer MG such that, for u > MG and u ≡ 1 or 3 (mod 6), there is a Steiner triple system U on u points for which AutU ∼= G. If V is a Steiner triple system then there is an integer NV such that, for u > NV and u ≡
Kantor, William M., Doyen, Jean
core   +1 more source

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 ...
Lucien Haddad, Vojtech Rödl
openaire   +1 more source

On the Trail of Creativity: Dimensionality of Divergent Thinking and Its Relation With Cognitive Abilities, Personality, and Insight

European Journal of Personality, EarlyView., 2020
Abstract Divergent thinking (DT) is an important constituent of creativity that captures aspects of fluency and originality. The literature lacks multivariate studies that report relationships between DT and its aspects with relevant covariates, such as cognitive abilities, personality traits (e.g. openness), and insight. In two multivariate studies (N 
S. Weiss, D. Steger, Y. Kaur, A. Hildebrandt, U. Schroeders, O. Wilhelm, Christian Kandler   +6 more
wiley   +1 more source

Nonsequenceable Steiner triple systems [PDF]

Bull. ICA, 2019
A partial Steiner triple system is is $sequenceable$ if the points can be sequenced so that no proper segment can be partitioned into blocks. We show that, if $0 \leq a \leq (n-1)/3$, then there exists a nonsequenceable PSTS$(n)$ of size $\frac{1}{3}\binom{n}{2}-a$, for all $n \equiv 1 \pmod{6}$ except for $n=7$.
Donald L. Kreher, Douglas R. Stinson
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Countable homogeneous Steiner triple systems avoiding specified subsystems [PDF]

, 2021
In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fraïssé limits of classes of finite Steiner triple systems avoiding certain subsystems.
Horsley, Daniel, Webb, Bridget S.
core   +1 more source

All proper colorings of every colorable BSTS(15) [PDF]

Computer Science Journal of Moldova, 2010
A Steiner System, denoted S(t,k,v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case
Jeremy Mathews, Brett Tolbert
doaj  

Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s [PDF]

Computer Science Journal of Moldova, 2011
A Bi-Steiner Triple System ($BSTS$) is a Steiner Triple System with vertices colored in such a way that the vertices of each block receive precisely two colors.
Jeremy Mathews
doaj