arXiv subjects

Yasiru Jayasooriya

Publications and source records attributed to Yasiru Jayasooriya.

2 recordsLinked to original sources

arXiv2023

Study of Exoo's Lower Bound for Ramsey number $R(5,5)$

We review Exoo's 1989 paper, which demonstrates that a lower bound for the Ramsey number $R(5,5)$ is $43$. We provide an efficient way to verify the claims in the paper, adding detailed proofs. In particular, we replace the reference to computer verification by concise arguments. Using our understanding of the insight behind these proofs, we are also able to analyse variations of the graph constructions to obtain, for example, colourings of $K_{43}$ which have very few monochromatic $K_5$.

math.CO↗

arXiv2023

Eigenvalue-less matrices from SL$_3(\mathbb{F}_7)$ to PSL$_3(\mathbb{F}_7)$

We analyse the set of matrices in SL$_3(\mathbb{F}_7)$ without eigenvalues explicitly, extracting nice bijections between the 18 equally sized conjugacy classes contained within. In doing so, we discover a set of $18$ commuting matrices for which every conjugacy class is represented and tells us how to decide when collections of commuting matrices are simultaneously conjugate. The main innovation is the proofs are accessible to undergraduates and do not rely on computer calculations nor very general theory. It is also rare that the details of special cases are written down.

math.GM↗