Titlebook: Combinatorial Mathematics IV; Proceedings of the F Louis R. A. Casse,Walter D. Wallis Conference proceedings 1976 Springer-Verlag Berlin He

leniency

Comma-free codes and incidence algebras,dering the binary relation the code defines on its alphabet. If the code is a maximal comma-free code we show that the relation it defines is the support relation of an incidence algebra and its complementary relation will also define an incidence algebra.

aspersion

An infinite family of skew weighing matrices,2.·7?1 in order 2.·7..We discuss the construction of orthogonal designs using circulant matrices. In particular we construct designs in orders 20 and 28..The weighing matrix conjecture is verified for order 60.

Meander

nominal

Bounds of finite relations, following holds: if no member of .is embeddable in R then R has a strict extension in which no member of .is embeddable. In fact, if all members of .are defined on sets with at least n elements this number N is 3.. . 2.-1 where s(n,k) are the Stirling numbers of the second kind.

Arboreal

Limited

fleeting

A non-imbeddable proper colouring,r colours. We say that this colouring, and all the complete subgraphs of it, are derived from the sum-free partition..It has been asked whether every triangle-free colouring of a complete graph in r colours can be derived from some sum-free partition into r parts. We prove that the answer is "no", b

padding

Number of factors in K-cycle decompositions of permutations,k-cycles. Denote by f.(π) the minimal number of k-cycles required for such a representation. In this paper bounds for f.(π) are derived. These bounds are used to determine . for all k, where f.(n)=max{f.(π) | π ε S.}.

projectile

cultivated

Designs from cyclotomy,lock designs. Our main construction method, using unions of cyclotomic classes, gives us upper bounds on m, the number of associate classes of the design, but not exact values for m; we discuss the possible values of m and the circumstances under which m=1, so that the design is in fact balanced.