Steiner quadruple systems - a survey

DOI10.1016/0012-365X(78)90122-XzbMath0398.05015OpenAlexW2032066269MaRDI QIDQ1254321

Charles C. Lindner, Alexander Rosa

Publication date: 1978

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(78)90122-x

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Combinatorial aspects of block designs (05B05) Steiner systems in finite geometry (51E10) Research exposition (monographs, survey articles) pertaining to geometry (51-02)

Related Items

Some remarks on the construction of cyclic Steiner quadruple systems, Egalitarian Steiner quadruple systems of doubly even order, The monochromatic block number, Combinatorial constructions of optimal \((m,n,4,2)\) optical orthogonal signature pattern codes, On complete arcs in Steiner systems S(2,3,v) and S(2,4,v), The Steiner quadruple systems of order 16, On Disjoint Partial Quadruple Systems having Seventeen Blocks, Construction of nilpotent sloops of class \(n\), Upper chromatic number of Steiner triple and quadruple systems, The number of the non-full-rank Steiner quadruple systems \(S ( v , 4 , 3 )\), Steiner triple systems \(S(2^m-1,3,2)\) of rank \(2^m-m+1\) over \(\mathbb F_2\), Intersections Among Ordered Quadruple Systems, Construction of Factorized Steiner Quadruple Systems of Order 16 with Blocking Sets, Classification of Cyclic Steiner Quadruple Systems, A possible analogue of \(\rho\)-labellings for 3-uniform hypergraphs, Algebras that represent Steiner systems through permutation groups., On affine-invariant two-fold quadruple systems, On the existence of ternary quasi-groups with two or eight conjugacy classes, Classification of Steiner quadruple systems of order 16 and rank 14, On resolvability of Steiner systems \(S ( v = 2^{ m }, 4, 3)\) of rank \(r \leq v - m + 1\) over \(\mathbb{F}_{2}\), Construction of Steiner quadruple systems having a prescribed number of blocks in common, Zero-sum flows for Steiner systems, Semi-planar Steiner loops of cardinality 2\(n\), Coordinate transitivity of a class of extended perfect codes and their SQS, A cyclic Steiner quadruple system of order 32, On the intersection of two S(3,4,2v) having a same derived triple system, Blocking sets in 3-designs, A construction of orthogonal arrays and applications to embedding theorems, On S-cyclic Steiner systems, A general recursive construction for quadruple systems, On the set \(J(v)\) for Steiner quadruple systems of order \(v=2^ n\) with \(n\geq 4\), Steiner systems and configurations of points, Cyclic Steiner quadruple systems and Köhler's orbit graphs, Some naive constructions of \(S(2,3,\nu{})\) and \(S(2,4,\nu{})\), Piotrowski's infinite series of Steiner quadruple systems revisited, Affine-invariant strictly cyclic Steiner quadruple systems, Intersections of Steiner quadruple systems, 2-colourings in \(S(t, t+1, v)\), Semiboolean SQS-skeins, Constructions for strictly cyclic 3-designs and applications to optimal OOCs with \(\lambda =2\), Structure of Steiner triple systems \(S(2^m-1,3,2)\) of rank \(2^m-m+2\) over \(\mathbb F_2\), Non-full-rank Steiner quadruple systems \(S(v,4,3)\), On disjoint partial triple systems, On one transformation of Steiner quadruple systems \(S(\upsilon , 4, 3)\), Vasil'ev codes of length \(n=2^m\) and doubling of Steiner systems \(S(n,4,3)\) of a given rank, Almost simple groups with socle \(L_n(q)\) acting on Steiner quadruple systems, Subdesigns in Steiner quadruple systems, Constructions of dihedral Steiner quadruple systems, Further results on existentially closed graphs arising from block designs, The family of block designs with some combinatorial properties, Constructions for generalized Steiner systems \(\mathrm{GS}(3,4,v,2)\), On semi-planar Steiner quasigroups, Constructions for cyclic 3-designs and improved results on cyclic Steiner quadruple systems, Steiner systems \(S(v, k, k - 1)\): components and rank, Classification of generalized ternary quadratic quasigroup functional equations of the length three, Pairwise Disjoint intersections Among Steiner Quadruple Systems, The family of t-designs. II, Partitions of the 4-subsets of a 13-set into disjoint projective planes, Intersection Theory for Embeddings of Matroids into Uniform Geometries, Constructions via Hamiltonian theorems, Classification of Steiner quadruple systems of order 16 and rank at most 13, The last packing number of quadruples, and cyclic SQS, Recursive constructions for cyclic block designs, Intersections of Steiner systems S(3,4,v) with \(v=5\cdot 2^ n\), The fundamental construction for 3-designs, Steiner quadruple systems having a prescribed number of quadruples in common

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the construction of cyclic quasigroups
• Steinersche Tripelsysteme mit fahnentransitiver Kollineationsgruppe
• Finite partial quadruple systems can be finitely embedded
• On the number of 1-factorizations of the complete graph
• A partial Steiner triple system of order n can be embedded in a Steiner triple system of order 6n + 3
• Some packings with Steiner triple systems
• A theorem on the maximum number of disjoint Steiner triple systems
• On the existence of automorphism free Steiner triple systems
• Finite embedding theorems for partial Steiner triple systems
• Equational classes of Steiner systems
• Partitioning the planes of \(AG_{2m}(2)\) into 2-designs
• Some sufficient conditions for a Steiner triple system to be a derived triple system
• Steiner quadruple systems all of whose derived Steiner triple systems are nonisomorphic
• Some derived Steiner triple systems
• On certain constructions for latin squares with no latin subsquares of order two
• The smallest non-derived Steiner triple system is simple as a loop
• Sur les systèmes de quadruples
• Intersections among Steiner systems
• Combinatorial designs and algebras
• Covering all triples on n marks by disjoint Steiner systems
• On coverings
• Fahnenhomogene Quadrupelsysteme
• Sur la structure de certains systèmes triples de Steiner
• Maximal and minimal coverings of (k - 1)-tuples by k-tuples
• The completion of finite incomplete Steiner triple systems with applications to loop theory
• On a technique for representing semigroups as endomorphism semigroups of graphs with given properties
• Embeddings of Steiner triple systems
• On the maximum number of disjoint Steiner triple systems
• On Quadruple Systems
• Construction of Steiner Quadruple Systems Having Large Numbers of Nonisomorphic Associated Steiner Triple Systems
• Some remarks on the Steiner triple systems associated with Steiner quadruple systems
• On the structure of the Steiner triple systems derived from the Steiner quadruple systems
• Construction of Large Sets of Almost Disjoint Steiner Triple Systems
• Tactical Configurations of Rank Two
• On the construction of non-isomorphic Steiner quadruple systems
• Some new constructions of 4-tuple systems
• On Some Tactical Configurations
• On one-factorizations of complete graphs