4 papers
An Improved Lower Bound for and Some Interesting Templates
Fred Rowley
In this simple paper, we exhibit a Schur partition giving rise to a triangle-free linear colouring of in 7 colours. Thus we show that the Schur number an…
New lower bounds for weak Schur partitions
Fred Rowley
This paper records some apparently new results for the partition of integer intervals [1, n] into weakly sum-free subsets. These were produced using a method closely related to tha…
A construction for weak Schur partitions
Fred Rowley
In 1952, J.H.Braun claimed to have established a formula giving a lower bound for certain partitions of sets of integers into weakly sum-free classes. However, no proof or supporti…
Some further results in Ramsey graph construction
Fred Rowley
A construction described by the current author (2017) uses two linear prototypes to build a compound graph with Ramsey properties inherited from the prototype graphs. The resulting…