Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.8

Counting Miura-ori Foldings

Jessica Ginepro
Department of Mathematics
University of Connecticut
196 Auditorium Road, Unit 3009
Storrs, CT 06269-3009

Thomas C. Hull
Department of Mathematics
Western New England University
1215 Wilbraham Road
Springfield, MA 01119


We consider the problem of enumerating the different ways in which the classic Miura map fold crease pattern can be folded flat. Specifically, we aim to count the number M(n,m) of ways to assign mountains and valleys to the creases so that each vertex in a m by n Miura map fold will be able to fold flat. Recurrence relations and closed formulas are found for small n and arbitrary m. We also prove that the array of numbers generated by M(n,m) is equivalent to the number of ways to properly 3-vertex-color a m × n grid graph with one vertex pre-colored.

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(Concerned with sequence A078099.)

Received July 4 2013; revised versions received July 17 2014; September 18 2014. Published in Journal of Integer Sequences, November 5 2014.

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