Jair Taylor

Formal Group Laws and Chromatic Symmetric Functions of Hypergraphs
dmtcs:2499 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2015,
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

https://doi.org/10.46298/dmtcs.2499
Formal Group Laws and Chromatic Symmetric Functions of Hypergraphs
Authors: Jair Taylor ^{1}
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Jair Taylor
1 University of Washington [Seattle]
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 Schurpositive.