On Quadruple Systems

DOI10.4153/CJM-1960-013-3zbMath0092.01202MaRDI QIDQ3267410

Haim Hanani

Publication date: 1960

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

combinatorics

Related Items (only showing first 100 items - show all)

Existence of optimal strong partially balanced 3-designs with block size four ⋮ Bounds on the number of edges of edge-minimal, edge-maximal and \(l\)-hypertrees ⋮ Some remarks on the construction of cyclic Steiner quadruple systems ⋮ Constructions of doubly resolvable Steiner quadruple systems ⋮ On the construction of \(t\)-designs and the existence of some new infinite families of simple 5-designs ⋮ On the 3BD-closed set \(B_3(\{4,5\})\) ⋮ Intersection problem of Steiner systems S(3,4,2v) ⋮ The monochromatic block number ⋮ Combinatorial constructions of optimal \((m,n,4,2)\) optical orthogonal signature pattern codes ⋮ The spectrum for large sets of pure directed triple systems ⋮ The existence of resolvable Steiner quadruple systems ⋮ A new existence proof for Steiner quadruple systems ⋮ Upper chromatic number of Steiner triple and quadruple systems ⋮ Exact coverings of 2-paths by 4-cycles ⋮ Steiner triple systems \(S(2^m-1,3,2)\) of rank \(2^m-m+1\) over \(\mathbb F_2\) ⋮ \(f\)-vectors of pure complexes and pure multicomplexes of rank three ⋮ The spectrum of \(G\)-\(\mathrm{OD}_{\lambda }(3,4,v)\) ⋮ Certain recurrent and asymptotic estimates in the covering problem ⋮ Overlarge sets of resolvable idempotent quasigroups ⋮ On affine-invariant two-fold quadruple systems ⋮ On projective and affine hyperplanes ⋮ Amalgamations of connected \(k\)-factorizations. ⋮ On the existence of ternary quasi-groups with two or eight conjugacy classes ⋮ The existence spectrum for overlarge sets of pure directed triple systems ⋮ The existence spectrum of Meta\((K^{(3)}_{4} > K^{(3)}_{4} - e)\) ⋮ 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 \(\mathbb{F}_{2}\) ⋮ The family of t-designs. Part I ⋮ Construction of Steiner quadruple systems having a prescribed number of blocks in common ⋮ 2-chromatic Steiner quadruple systems ⋮ \((1,2)\)-resolvable candelabra quadruple systems and Steiner quadruple systems ⋮ On the minimum number of blocks of a maximal partial spread in STS(v) and SQS(v) ⋮ On the intersection of two S(3,4,2v) having a same derived triple system ⋮ Systems of pairs of cyclic type ⋮ Blocking sets in 3-designs ⋮ Orthogonal quadruple systems and 3-frames ⋮ On the structure of the \(h\)-vector of a paving matroid ⋮ Quadruple systems containing \(AG(3,2)\) ⋮ On S-cyclic Steiner systems ⋮ H-designs with the properties of resolvability or (1, 2)-resolvability ⋮ A general recursive construction for quadruple systems ⋮ Optimal \((n,4,2)\)-OOC of small orders. ⋮ On the set \(J(v)\) for Steiner quadruple systems of order \(v=2^ n\) with \(n\geq 4\) ⋮ Optimal ternary constant-composition codes with weight four and distance three ⋮ The spectrum of tetrahedral quadruple systems ⋮ A new class of 3-fold perfect splitting authentication codes ⋮ Optimal constant weight covering codes and nonuniform group divisible 3-designs with block size four ⋮ Intersections and supports of quadruple systems ⋮ Optimal partitions for triples ⋮ The completion determination of optimal \((3,4)\)-packings ⋮ Piotrowski's infinite series of Steiner quadruple systems revisited ⋮ The spectrum for large sets of pure Mendelsohn triple systems ⋮ Affine-invariant strictly cyclic Steiner quadruple systems ⋮ Intersections of Steiner quadruple systems ⋮ 2-colourings in \(S(t, t+1, v)\) ⋮ Constructions for strictly cyclic 3-designs and applications to optimal OOCs with \(\lambda =2\) ⋮ Forbidden configurations and Steiner designs ⋮ The last twenty orders of (1,2)-resolvable Steiner quadruple systems ⋮ Support sizes of threefold quadruple systems ⋮ Candelabra systems and designs ⋮ Combinatorial constructions of fault-tolerant routings with levelled minimum optical indices ⋮ Disjoint finite partial Steiner triple systems can be embedded in disjoint finite Steiner triple systems ⋮ The existence of augmented resolvable Steiner quadruple systems ⋮ Large sets of disjoint packings on \(6k+5\) points ⋮ Suitable sets of permutations, packings of triples, and Ramsey's theorem ⋮ Finite embedding theorems for partial Steiner triple systems ⋮ Zur Theorie der Steinersysteme ⋮ 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 ⋮ List decodability at small radii ⋮ Almost simple groups with socle \(L_n(q)\) acting on Steiner quadruple systems ⋮ Two finite embedding theorems for partial 3-quasigroups ⋮ Constructions and bounds for separating hash families ⋮ Totally symmetric and semi-symmetric quasigroups have the intersection preserving finite embeddability property ⋮ The smallest non-derived Steiner triple system is simple as a loop ⋮ Constructions of dihedral Steiner quadruple systems ⋮ Steiner quadruple systems - a survey ⋮ A note on partial parallel classes in Steiner systems ⋮ Minimal covering and maximal packing of (k-1)-subsets by k-subsets ⋮ 2-idempotent 3-quasigroups with a conjugate invariant subgroup consisting of a single cycle of length four. ⋮ Zyklische Quadrupelsysteme ⋮ On Steiner spaces ⋮ On the original Steiner systems ⋮ Steiner systems \(S(v, k, k - 1)\): components and rank ⋮ Existence of Steiner quadruple systems with a spanning block design ⋮ Arboricity: an acyclic hypergraph decomposition problem motivated by database theory ⋮ Infinite families of strictly cyclic Steiner quadruple systems ⋮ Existence of good large sets of Steiner triple systems ⋮ Uniformly resolvable three-wise balanced designs with block sizes four and six ⋮ Some \(t\)-designs are minimal \((t+1)\)-coverings ⋮ Combinatorial designs and algebras ⋮ A simple construction of disjoint and almost disjoint Steiner triple systems ⋮ An elementary approach to polynomial interpolation in universal algebras ⋮ On large sets of disjoint Steiner triple systems. IV ⋮ The last packing number of quadruples, and cyclic SQS ⋮ 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 ⋮ Some new 2-resolvable Steiner quadruple systems ⋮ Covering triples by quadruples: an asymptotic solution

This page was built for publication: On Quadruple Systems