Geodesic
Chromatic symmetric functions of hypertrees
Jair Taylor1
1University of Washington
The electronic journal of combinatorics, Tome 24 (2017) no. 2
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The chromatic symmetric function $X_H$ of a hypergraph $H$ is the sum of all monomials corresponding to proper colorings of $H$. When $H$ is an ordinary graph, it is known that $X_H$ is positive in the fundamental quasisymmetric functions $F_S$, but this is not the case for general hypergraphs. We exhibit a class of hypergraphs $H$ — hypertrees with prime-sized edges — for which $X_H$ is $F$-positive, and give an explicit combinatorial interpretation for the $F$-coefficients of $X_H$.
DOI : 10.37236/5369
Classification : 05E05, 05C65, 05C15
Mots-clés : symmetric function, quasisymmetric function, chromatic symmetric function, graph colouring, hypergraph, hypertree

Jair Taylor  1

1 University of Washington 
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     author = {Jair Taylor},
     title = {Chromatic symmetric functions of hypertrees},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {2},
     doi = {10.37236/5369},
     zbl = {1361.05138},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5369/}
}
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Jair Taylor. Chromatic symmetric functions of hypertrees. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/5369

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