Joseph Cooper

collaborators

4 papers

math.CO2024

Hyper-bishops, Hyper-rooks, and Hyper-queens: Percentage of Safe Squares on Higher Dimensional Chess Boards

Caroline Cashman, Joseph Cooper, Raul Marquez +2

The $n$ queens problem considers the maximum number of safe squares on an $n \times n$ chess board when placing $n$ queens; the answer is only known for small $n$ . Miller, Sheng an…

math.CO2024

Congruence Classes of Simplex Structures in Finite Field Vector Spaces

Timothy Cheek, Joseph Cooper, Pico Gilman +6

We study a generalization of the Erdős-Falconer distance problem over finite fields. For a graph $G$ , two embeddings $p, p^{'} : V (G) \to F_{q}^{d}$ of a graph $G$ are congruent i…

math.CO2024

Variants of Conway Checkers and k-nacci Jumping

Glenn Bruda, Joseph Cooper, Kareem Jaber +2

Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the c…

math.CO2015

A recurrence for an expression involving double factorials

Joseph E. Cooper

We find a closed-form solution to the recurrence $z_{n + 2} = \frac{1}{z _{n + 1}} + z_{n}$ , where $n \in Z_{\geq 1}$ and $z_{1} \in R_{> 0}, z_{2} \in R_{> 0}$ . As…