Geodesic
Formal Group Laws and Chromatic Symmetric Functions of Hypergraphs
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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If $f(x)$ is an invertible power series we may form the symmetric function $f(f^{-1}(x_1)+f^{-1}(x_2)+...)$ which is called a formal group law. We give a number of examples of power series $f(x)$ that are ordinary generating functions for combinatorial objects with a recursive structure, each of which is associated with a certain hypergraph. In each case, we show that the corresponding formal group law is the sum of the chromatic symmetric functions of these hypergraphs by finding a combinatorial interpretation for $f^{-1}(x)$. We conjecture that the chromatic symmetric functions arising in this way are Schur-positive. 
@article{DMTCS_2015_special_285_a43,
     author = {Taylor, Jair},
     title = {Formal {Group} {Laws} and {Chromatic} {Symmetric} {Functions} of {Hypergraphs}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2499},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2499/}
}
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Taylor, Jair. Formal Group Laws and Chromatic Symmetric Functions of Hypergraphs. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2499. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2499/

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