@article{814a5e2c80534bcc800dac33ad703b8a,

title = "Differential algebra of cubic planar graphs",

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 Fq-rational points of its graded augmentation variety are shown to coincide with (q+1)-colorings of the dual graph.",

keywords = "Binary sequence, Chromatic polynomial, Cubic planar graph, Differential algebra, Legendrian surface",

author = "Roger Casals and Emmy Murphy",

note = "Funding Information: Acknowledgments : K. Sackel is grateful Bjorn Poonen for pointing towards EGA. This work is supported by an NSF Graduate Research Fellowship. Funding Information: Acknowledgments: We thank the referee for his careful reading and helpful comments. We are grateful to Maxime Gabella, Richard Stanley, David Treumann and Eric Zaslow for useful conversations. R. Casals is supported by the NSF grant DMS-1841913 and a BBVA Research Fellowship and E. Murphy is partially supported by NSF grant DMS-1510305 and a Sloan Research Fellowship. E. Murphy would like to thanks the Radcliffe Institute of Advanced Studies where part of the article was written while in residence. Publisher Copyright: {\textcopyright} 2018",

year = "2018",

month = nov,

day = "7",

doi = "10.1016/j.aim.2018.09.002",

language = "English (US)",

volume = "338",

pages = "401--446",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}