J. Rooney

collaborators

2 papers

math.CO2025

Ramsey numbers of grid graphs

Xiaoyu He, Ghaura Mahabaduge, Krishna Pothapragada +2

Let the grid graph $G_{M \times N}$ denote the Cartesian product $K_{M} □ K_{N}$ . For a fixed subgraph $H$ of a grid, we study the off-diagonal Ramsey number $\operatorname{gr}(H,…

math.CO2025

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice

Joshua Rooney

For a positive integer $n$ , an $n$ -tuple of dice $(A_{1}, A_{2}, \dots, A_{n})$ is called balanced if $P (A_{1} < A_{2}) = P (A_{2} < A_{3}) = \dots = P (A_{n} < A_{1})$ and nontransitive if $P(A_1<A_2), P(A_2…