Vishal Balaji

collaborators

2 papers

math.CO2021

Schur's theorem in integer lattices

Vishal Balaji, Andrew Lott, Alex Rice

A standard proof of Schur's Theorem yields that any $r$ -coloring of ${1, 2, \dots, R_{r} - 1}$ yields a monochromatic solution to $x + y = z$ , where $R_{r}$ is the classical $r$ -color Ramsey…

math.CO2021

The pigenhole principle and multicolor Ramsey numbers

Vishal Balaji, Powers Lamb, Andrew Lott +4

For integers $k, r \geq 2$ , the diagonal Ramsey number $R_{r} (k)$ is the minimum $N \in N$ such that every $r$ -coloring of the edges of a complete graph on $N$ vertices yields o…