### Abstract

In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In addition, in the appendix by K. Sackel the F_{q}-rational points of its graded augmentation variety are shown to coincide with (q+1)-colorings of the dual graph.

Original language | English (US) |
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Pages (from-to) | 401-446 |

Number of pages | 46 |

Journal | Advances in Mathematics |

Volume | 338 |

DOIs | |

State | Published - Nov 7 2018 |

### Keywords

- Binary sequence
- Chromatic polynomial
- Cubic planar graph
- Differential algebra
- Legendrian surface

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Casals, R., & Murphy, E. (2018). Differential algebra of cubic planar graphs.

*Advances in Mathematics*,*338*, 401-446. https://doi.org/10.1016/j.aim.2018.09.002