2 citations · 3 across the 6 of their papers we have counts for
6 papers
Pandiagonal Type-p Franklin Squares
John Lorch
For prime we define magic squares of order , called type- Franklin squares, whose properties specialize to those of classical Franklin squares in the case . We co…
Linear Type-p Most-Perfect Squares
John Lorch
We describe a generalization of most-perfect magic squares, called type-p most-perfect squares, and in prime-power orders we give a linear construction of these squares reminiscent…
Constructing Ordered Orthogonal Arrays via Sudoku
John Lorch
For prime powers q we use "strongly orthogonal" linear Sudoku solutions of order q^2 to construct ordered orthogonal arrays of type OOA (4,s,2,q), and for each q we present a range…
A quick construction of mutually orthogonal sudoku squares
John Lorch
For any odd prime power q we provide a quick construction of a complete family of q(q-1) mutually orthogonal sudoku squares of order q^2.
Nest graphs and minimal complete symmetry groups for magic Sudoku variants
Elizabeth Arnold, Rebecca Field, John Lorch +2
A symmetry group for Sudoku is complete if its action partitions the set of Sudoku boards into all possible orbits, and minimal if no group of smaller size would do the same. Previ…
Inversion of an integral transform and ladder representations of U(1,q)
John D. Lorch, Lisa A. Mantini
An integral transform for G=U(1,q) is studied. The transform maps the positive spin ladder representations of G on a Bargmann-Segal-Fock space F_n^1,q into a space of polynomial-va…