@book{Background,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}olume 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second edition},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626}, 
}

@article{BN,
title = {Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function},
journal = {Discrete Mathematics},
volume = {343},
number = {10},
pages = {111989},
year = {2020},
doi = {https://doi.org/10.1016/j.disc.2020.111989},
author = {Bernardi, O. and Nadeau, P.},
keywords = {Acyclic orientations, Derivatives of the chromatic polynomial, Heaps},
abstract = {Let G be a graph, and let χG be its chromatic polynomial. For any non-negative integers i,j, we give an interpretation for the evaluation χG(i)(−j) in terms of acyclic orientations. This recovers the classical interpretations due to Stanley and to Greene and Zaslavsky respectively in the cases i=0 and j=0. We also give symmetric function refinements of our interpretations, and some extensions. The proofs use heap theory in the spirit of a 1999 paper of Gessel.}
}

@article{GZ,
    author = {Greene, C. and Zaslavsky, T.},
    title = {On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs},
  journal = {Transactions of the American Mathematical Society},
    year = {1983},
    volume = {280},
    number = {1},
    pages = {97--126},
       DOI = {10.2307/1999604},
}

@article{LP,
title = {Euclidean matchings and minimality of hyperplane arrangements},
journal = {Discrete Mathematics},
volume = {344},
number = {3},
pages = {112232},
year = {2021},
doi = {https://doi.org/10.1016/j.disc.2020.112232},
author = {Lofano, D. and Paolini, G.},
keywords = {Hyperplane arrangements, Discrete Morse theory},
abstract = {We construct a new class of maximal acyclic matchings on the Salvetti complex of a locally finite hyperplane arrangement. Using discrete Morse theory, we then obtain an explicit proof of the minimality of the complement. Our construction provides interesting insights also in the well-studied case of finite arrangements, and gives a nice geometric description of the Betti numbers of the complement. In particular, we solve a conjecture of Drton and Klivans on the characteristic polynomial of finite reflection arrangements. The minimal complex is compatible with restrictions, and this allows us to prove the isomorphism of Brieskorn’s Lemma by a simple bijection of the critical cells. Finally, in the case of line arrangements, we describe the algebraic Morse complex which computes the homology with coefficients in an abelian local system.}
}

@article{Kabluchko,
    author = {Kabluchko, Z.},
    title = {An Identity for the Coefficients of Characteristic Polynomials of Hyperplane Arrangements},
    journal = {Discrete and Computational Geometry},
    year = {2023},
    volume = {70},
    issue = {4},
    pages = {1476=1498}
}

@incollection{BG2,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {An introduction to hyperplane arrangements},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {389--496},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007}, 
       DOI = {10.1090/pcms/013/08},
       URL = {https://doi.org/10.1090/pcms/013/08},
}

@article{NUI,
title = {Chromatic posets},
journal = {Journal of Combinatorial Theory, Series A},
volume = {184},
pages = {105496},
year = {2021},
doi = {https://doi.org/10.1016/j.jcta.2021.105496},
author = {Dahlberg, S. and She, A. and {van Willigenburg}, S.},
keywords = {Chromatic symmetric function, Elementary symmetric function, Schur function, Positivity},
abstract = {In 1995 Stanley introduced the chromatic symmetric function XG of a graph G, whose e-positivity and Schur-positivity has been of large interest. In this paper we study the relative e-positivity and Schur-positivity between connected graphs on n vertices. We define and investigate two families of posets on distinct chromatic symmetric functions. The relations depend on the e-positivity or Schur-positivity of a weighed subtraction between XG and XH. We find a biconditional criterion between e-positivity or Schur-positivity and the relation to the complete graph. This gives a new paradigm for e-positivity and for Schur-positivity. We show many other interesting properties of these posets including that the family of trees forms an independent set and are maximal elements. Additionally, we find that stars are independent elements, the independence number increases as we increase in the poset and that the family of lollipop graphs forms a chain.}
}