
A basis is exhibited for the first homology space of a surface over a field. This basis is found by extending a basis of the boundary cycle space of an embedded graph to the cycle space of the graph.
Some interesting implications of the multiplier conjecture are pointed out in this paper. We show the nonexistence of seven unknown difference sets, assuming the multiplier conjecture. If any of those difference sets is found by other means, it would, therefore, disprove the multiplier conjecture. These difference sets correspond to seven missing entries in Lander’s table.
Groups
We show that there are
The cycle rank,
We prove that for any odd positive integer
In this paper, we examine the concept of cohesion, which was first introduced in
Let
Frames with
We give a brief account of some recent results on edge-colouring simple graphs and of some recent results on the total-chromatic number of simple graphs. We illustrate the kind of arguments which have been found to be successful by proving one of the simpler results on edge-colouring graphs, and by showing how to apply this to obtain one of the recent results on the total-chromatic number.
The question of whether all
A binary code has bounded synchronization delay if there exists an integer
A degree sequence which is realisable by a
We prove that if
Ideas are described that speed up the lattice basis reduction algorithm of Lenstra, Lenstra, and Lovász
It is shown that the collection of all
Suppose that one is given
The number of blocks in such a minimal design is denoted by the symbol
Recent examples of perfect 1-factorizations arising from dicyclic groups have led to the question of whether or not dicyclic groups have symmetric sequencings. For every positive integer
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