John Lorch

About

I'm a mathematics professor at Ball State University, where I've been employed since 1998. I received my Ph.D. in 1995 at Oklahoma State University.

email: jlorch at bsu dot edu

office: Robert Bell 473

Mathematical Interests

I'm currently interested in combinatorial designs, including Latin squares, Sudoku, and magic squares. I typically use algebraic techniques to construct and count such objects. Or, as Jeff Dinitz says, I like to put numbers in boxes. 

Here are some of my recent publications:

• J. Lorch, Doubly orthogonal equi-squares and sliced orthogonal arrays, preprint.

• J. Hammer and J. Lorch, Diagonal cellular factor pair Latin squares, Des. Codes Cryptogr. 91 (2023) 2309--2322.

• J. Decapua and J. Lorch, Sudoku pair Latin squares based on groups, Discrete Math. 345 no. 6 (2022) 112852.

• B. Carrigan, D. Diaz, J. Hammer, J. Lorch, and R. Lorch, Constructing (3,b)-Sudoku pair Latin squares,  Australas. J. Combin 82 no. 1 (2022), 31--58.

• B. Carrigan, J. Hammer, J. Lorch, R. Lorch, and C. Owens, List colorings count Rokudoku-pair squares, Bull. ICA  92 (2021), 62--77.

• B. Carrigan, J. Hammer, and J. Lorch, A regional Kronecker product and multiple-pair Latin squares, Discrete Math. 343 no. 3 (2020) 111762.

• J. Hammer and J. Lorch,  Orthogonal factor-pair Latin squares of prime-power order, J. Combin. Des.  27 no. 9 (2019), 552--561.

• J. Lorch,  Pandiagonal type-p Franklin squares, Australas. J. Combin. 73 (2019), 84--106.

• J. Lorch,  Generalized most-perfect squares, Congr. Numer. 230 (2018), 249--259.

• R. Bremigan and J. Lorch, Mutually orthogonal rectangular gerechte designs,  Linear Algebra Appl. 497 (2016), 44--61.

• J. Lorch, Constructing ordered orthogonal arrays via sudoku, J. Algebra Appl. 15 no. 8 (2016) 1--19.

• E. Arnold, R. Field, J. Lorch, S. Lucas, and L. Taalman, Nest graphs and minimal complete symmetry groups for magic sudoku variants, Rocky Mountain J. Math. 45 no. 3 (2015) 887--901.

• J. Lorch, Linear magic rectangles, Linear Multilinear Algebra 62 no. 4 (2014), 530--537.

Teaching

I have enjoyed teaching a wide variety of courses over my career, from introductory to graduate level. The list includes college algebra, trigonometry, elementary statistics, single- and multi-variable calculus, linear algebra, differential equations, discrete mathematics, modern geometries, mathematical modeling, abstract algebra, coding and communication, real analysis, complex analysis, the history of mathematics, mathematics for elementary teachers, and secondary school mathematics from an advanced viewpoint. The development and instruction of this latter course motivated Mathematics for Secondary School Teachers  (MAA Press, 2011, with Ralph Bremigan and Elizabeth Bremigan).

My current teaching schedule can be found here.