Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.4

On the Maximum Number of Non-intersecting Diagonals in an Array

Peter Boyland
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Gabriella Pintér and István Laukó
Department of Mathematical Sciences
University of Wisconsin-Milwaukee
Milwaukee, WI 53211

Ivan Roth
Department of Mathematics, Statistics and Computer Science
Marquette University
Milwaukee, WI 53233

Jon E. Schoenfield
Huntsville, AL

Stephen Wasielewski
Rufus King International School - High School
Milwaukee, WI 53209


We investigate the total number of diagonals that can be placed in the unit squares of a given grid in such a way that no two diagonals have a common point. We develop theoretical and computational results for square and rectangular shaped grids, and extend the problem to three-dimensional arrays. We pose some open questions for further investigation.

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(Concerned with sequences A260690 A264041.)

Received July 25 2016; revised versions received November 13 2016; December 2 2016; December 5 2016. Published in Journal of Integer Sequences, December 27 2016.

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