Popularity Block Labelling for Steiner Systems

Intersection triangles and block intersection numbers of Steiner systems

Mathematische Zeitschrift ◽

10.1007/bf01418308 ◽

1974 ◽

Vol 139 (2) ◽

pp. 87-104 ◽

Cited By ~ 14

Author(s):

Benedict H. Gross

Keyword(s):

Steiner Systems ◽

Intersection Numbers ◽

Block Intersection

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Covering all triples on n marks by disjoint Steiner systems

Journal of Combinatorial Theory Series A ◽

10.1016/0097-3165(73)90082-4 ◽

1973 ◽

Vol 15 (3) ◽

pp. 347-350 ◽

Cited By ~ 28

Author(s):

Shmuel Schreiber

Keyword(s):

Steiner Systems

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On block-schematic Steiner systems $S(t,t+2,v)$ and $S(t,t+3,v)$

Hokkaido Mathematical Journal ◽

10.14492/hokmj/1381517494 ◽

1990 ◽

Vol 19 (3) ◽

pp. 481-493

Author(s):

Mitsuo YOSHIZAWA

Keyword(s):

Steiner Systems

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Finite Geometric Spaces, Steiner Systems and Cooperative Games

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2014-0015 ◽

2014 ◽

Vol 22 (1) ◽

pp. 189-205 ◽

Cited By ~ 10

Author(s):

Antonio Maturo ◽

Fabrizio Maturo

Keyword(s):

Cooperative Games ◽

Steiner Systems ◽

Affine Planes

AbstractSome relations between finite geometric spaces and cooperative games are considered. The games associated to Steiner systems, in particular projective and affine planes, are considered. The properties of winning and blocking coalitions are investigated.

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Direct Product of Derived Steiner Systems Using Inversive Planes

Canadian Journal of Mathematics ◽

10.4153/cjm-1981-105-7 ◽

1981 ◽

Vol 33 (6) ◽

pp. 1365-1369 ◽

Cited By ~ 2

Author(s):

K. T. Phelps

Keyword(s):

Direct Product ◽

Triple System ◽

Steiner Triple System ◽

Steiner System ◽

Steiner Systems

A Steiner system S(t, k, v) is a pair (P, B) where P is a v-set and B is a collection of k-subsets of P (usually called blocks) such that every t-subset of P is contained in exactly one block of B. As is well known, associated with each point x ∈ P is a S(t � 1, k � 1, v � 1) defined on the set Px = P\{x} with blocksB(x) = {b\{x}|x ∈ b and b ∈ B}.The Steiner system (Px, B(x)) is said to be derived from (P, B) and is called (obviously) a derived Steiner (t – 1, k – 1)-system. Very little is known about derived Steiner systems despite much effort (cf. [11]). It is not even known whether every Steiner triple system is derived.Steiner systems are closely connected to equational classes of algebras (see [7]) for certain values of k.

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