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Doubly and orthogonally resolvable quadruple systems

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 829)

Abstract

A Steiner system (X,β), denoted Sλ(t,k,v), is a set X of points, of cardinality v, and a collection β of k-subsets of X called blocks, with the property that every t-subset of X is contained in precisely λ blocks. A quadruple system of order v is a Steiner system S1(3,4,v). A triple (X,β,γ) is called an (s,μ)-resolvable system if for some s<t, it is a partition of an Sλ(t,k,v) system (X,β) into subsystems (X,γi), each of which is an Sμ(s,k,v) system with γ=γ12|…|γc being a partition of β. An (s,μ)-resolvable system (X,β,γ) is (s,μ)(r,v)-doubly resolvable if each (X,γi) is (r,v)-resolvable. Two (1,1)-resolvable Steiner systems (X,β,γ) and (X,β,γ′) are orthogonal if |γi ∩ γ′j|⩽1 for all i and j. This paper contains constructions of (2,3)(1,1)-doubly resolvable quadruple systems of orders v = 20,32,44, 68,80 and 104; a(2,3)-resolvable quadruple system of order 128; and some sets of mutually orthogonal resolutions of quadruple systems of all the above orders.

Keywords

  • Prime Power
  • Parallel Class
  • Quadratic Residue
  • Steiner System
  • Quadruple System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work forms part of the author’s research towards a Ph.D. at the University of Newcastle.

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© 1980 Springer-Verlag

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Hartman, A. (1980). Doubly and orthogonally resolvable quadruple systems. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088909

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  • DOI: https://doi.org/10.1007/BFb0088909

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