# Coloring connections with counting mountain-valley assignments

arXiv: https://arxiv.org/abs/1601.02727 · HTML: https://mlsanity.com/paper/1601.02727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2016.

## Built on by (most cited first, 1 of 1)

- [OrigamiSet1.0: Two New Datasets for Origami Classification and Difficulty Estimation](https://mlsanity.com/paper/2101.05470/) (2021)

## Abstract (arXiv)

We survey more recent attempts at enumerating the number of mountain-valley assignments that allow a given crease pattern to locally fold flat. In particular, we solve this problem for square twist tessellations and generalize the method used to a broader family of crease patterns. We also describe the more difficult case of the Miura-ori and a recently-discovered bijection with 3-vertex colorings of grid graphs.