Geodesic
An extension of Stanley's symmetric acyclicity theorem to signed graphs
Oscar Coppola1 ; Jake Huryn2 ; Michael Reilly2
1University of Maryland
2The Ohio State University
The electronic journal of combinatorics, Tome 31 (2024) no. 3
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In 1995, Richard P. Stanley introduced the chromatic symmetric function $X_G$ of a graph $G$ and proved that, when written in terms of the elementary symmetric functions, it reveals the number of acyclic orientations of $G$ with a given number of sinks. In this paper, we generalize this result to signed graphs, that is, to graphs whose edges are labeled with $+$ or $-$ and whose colorings and orientations can interact with their signs.Additionally, we introduce a non-homogeneous basis which detects the number of sinks and which not only gives a Stanley-type result for signed graphs, but gives an analogous result of this form for unsigned graphs as well.
DOI : 10.37236/12563
Classification : 05C22, 05C31, 05C15, 05E05
Mots-clés : chromatic symmetric function, Stanley-type result for signed graphs

Oscar Coppola  1   ; Jake Huryn  2   ; Michael Reilly  2

1 University of Maryland
2 The Ohio State University 
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Oscar Coppola; Jake Huryn; Michael Reilly. An extension of Stanley's symmetric acyclicity theorem to signed graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12563

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