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
USA

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

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

Jon E. Schoenfield
Huntsville, AL
USA

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

Abstract:

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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