Geodesic
Flows on Simplicial Complexes
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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Given a graph $G$, the number of nowhere-zero $\mathbb{Z}_q$-flows $\phi _G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\mathbb{Z} _q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes. 
@article{DMTCS_2012_special_263_a71,
     author = {Beck, Matthias and Kemper, Yvonne},
     title = {Flows on {Simplicial} {Complexes}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3085},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3085/}
}
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Beck, Matthias; Kemper, Yvonne. Flows on Simplicial Complexes. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3085. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3085/

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