Halving Steiner triple systems

Balanced Steiner Triple Systems

✍ Charles Colbourn; Lucien Haddad; Václav Linek 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 302 KB

and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press ## 1. Introduction A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that eve

Bicyclic Steiner triple systems

✍ Rebecca Calahan-Zijlstra; Robert B. Gardner 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 467 KB

Unbalanced steiner triple systems

✍ Lucien Haddad; Vojtech Rödl 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 653 KB

Skew-orthogonal steiner triple systems

✍ P. Dukes; E. Mendelsohn 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 302 KB 👁 1 views

Two Steiner triple systems, S 1 VY B 1 and S 2 VY B 2 , are orthogonal (S 1 c S 2 ) if B 1 B 2 Y and if fuY vg T fxY yg, uvwY xyw P B 1 , uvsY xyt P B 2 then s T t. The solution to the existence problem for orthogonal Steiner triple systems, (OSTS) was a major accomplishment in design theory. Two or

Embeddings of Steiner triple systems

✍ Jean Doyen; Richard M. Wilson 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 867 KB

If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i

On reverse Steiner triple systems

✍ Alexander Rosa 📂 Article 📅 1972 🏛 Elsevier Science 🌐 English ⚖ 950 KB

1 he existence of reverse Steiner triple systems It.e. Steiner triple systems with a given involutory automorphism of speck4 type) is investigated. it is srfrwrn that such a system exists far alI wders n if n z t of 3 or 9 (mod 24: except posd&ly far n = 25. A system with this grspetty exists also f