
Let
Stinson and van Rees have shown that under certain circumstances, critical sets in Latin squares
We obtain necessary conditions for the enclosing of a group divisible design with block size 3,
A known convolution identity involving the Catalan numbers is presented and discussed. Catalan’s original formulation, which is algebraically straightforward, is similar in style to one reported previously by the first author and the result has some interesting combinatorial aspects.
In this paper we prove various properties of the meanders. We then use these properties in order to construct recursively the set of all meanders of any particular order.
The main results of this paper are the discovery of infinite families of flow equivalent pairs of
Agrawal provided a construction for designs for two-way elimination of heterogeneity, based on a symmetric balanced incomplete block design. He could not prove the construction, although he found no counterexample. Subsequently Raghavarao and Nageswarerao published a proof of the method. In this note we observe a flaw in the published proof.
We discuss van der Waerden’s theorem on arithmetic progressions and an extension using Ramsey’s theorem, and the canonical versions. We then turn to a result (Theorem 6 below) similar in character to van der Waerden’s theorem, applications of Theorem 6, and possible canonical versions of Theorem 6. We mention several open questions involving arithmetic progressions and other types of progressions.
Let
Consider a graph
A technique is described that constructs a 4-colouring of a planar triangulation in quadratic time. The method is based on iterating Kempe’s technique. The heuristic gives rise to an interesting family of graphs which cause the algorithm to cycle. The structure of these graphs is described. A modified algorithm that appears always to work is presented. These techniques may lead to a proof of the 4-Colour Theorem which does not require a computer to construct and colour irreducible configurations.
For
is a constant map. We denote the set of all
A graph
It is known that if a
In this paper, an outline of the method used to search the weight 12 words of these codes is given. The paper also gives estimations on the size of the search space for the remaining 179 codes. Special attention is paid to the toughest cases, namely the 11 codes that contain 0 weight 4 words and the 21 codes that contain one and only one weight 4 word.
Given a polyomino
De Launey and Seberry have looked at the existence of Generalized Bhaskar Rao designs with block size 4 signed over elementary Abelian groups and shown that the necessary conditions for the existence of a
1970-2025 CP (Manitoba, Canada) unless otherwise stated.