Peter Dukes

collaborators

3 papers

math.CO2026

Fuzzy latin squares and balanced permutation pattern statistics

Joy Cooper, Peter J. Dukes

A latin square of order $n$ can be viewed as a partition of the $n \times n$ all-ones matrix into permutation matrix summands. Here, we consider a relaxation in which the matrix su…

math.CO2026

Intersection numbers of Sudoku latin squares

Jade S. Davies, Peter J. Dukes

Let $n = h w$ , where $h$ and $w$ are integers with $h, w \geq 2$ . We determine the set of possible intersection numbers of two $n \times n$ latin squares having the additional `Sudoku'…

math.CO2024

The balancing index over the alternating group

Peter Dukes, Georgia Penner

The balancing index of a polynomial $f \in Z [x_{1}, \dots, x_{n}]$ is the least positive sum of coefficients in an integer linear combination of permuted copies of $f$ which pro…