@misc{UchiumiYoshinaga,
      AUTHOR = {Uchiumi, R. and Yoshinaga, M.},
      EPRINT = {2409.01084},
  EPRINTTYPE = {arXiv},
       TITLE = {The quasi-polynomiality of mod $q$ permutation representation for a linear finite group action on a lattice},
        YEAR = {2024}}

@book{BeckRobins,
	author = {Beck, M. and Robins, S.},
	title = {Computing the continuous discretely},
	address = {Berlin, Heidelberg},
	series = {Undergraduate Texts in Mathematics},
	volume = {285},
    doi = {10.1007/978-0-387-46112-0}, 
	publisher = {Springer New York},
	year = {2007},
    month = oct
}

@article{KamiyaTakemuraTerao,
	author = {Kamiya, H. and Takemura, A. and Terao, H.},
	title = {Periodicity of hyperplane arrangements with integral coefficients modulo positive integers},
	volume = {27},
	doi = {10.1007/s10801-007-0091-2},
	number = {3},
	journal = {Journal of Algebraic Combinatorics},
	month = may,
	year = {2008},
	pages = {317--330}
}

@article{Stapledon,
	author = {Stapledon, A.},
	title = {Equivariant Ehrhart theory},
	volume = {226},
	doi = {10.1016/j.aim.2010.10.019},
	number = {4},
	journal = {Advances in Mathematics},
	month = mar,
	year = {2011},
	pages = {3622--3654}
}

@article{Carter,
     author = {Carter, R. W.},
     title = {Conjugacy classes in the Weyl group},
     journal = {Compositio Mathematica},
     pages = {1--59},
     publisher = {Wolters-Noordhoff Publishing},
     volume = {25},
     number = {1},
     year = {1972},
     mrnumber = {318337},
     zbl = {0254.17005},
     language = {en},
     url = {http://www.numdam.org/item/CM_1972__25_1_1_0/}
}

@article{Young,
	author = {Young, A.},
	title = {On Quantitative Subsituational Analysis},
	volume = {s2-31},
	doi = {10.1112/plms/s2-31.1.273},
	journal = {Proceedings of the London Mathematical Society},
	year = {1930},
	pages = {273--288}
}

@book{Weyl,
	author = {Weyl, H.},
	title = {The Classical Groups: Their Invariants and Representations},
	address = {Princeton},
	volume = {},
    doi = {10.1515/9781400883905}, 
	publisher = {Princeton University Press},
	year = {1946}
}

@article{ShephardTodd,
	author = {Shephard, G. C. and Todd, J. A.},
	title = {Finite Unitary Reflection Groups},
	volume = {6},
	doi = {10.4153/CJM-1954-028-3},
	journal = {Canadian Journal of Mathematics},
	year = {1954},
	pages = {274--304}
}

@article{OrlikSolomonTerao,
	author = {Orlik, P. and Solomon, L. and Terao, H.},
	title = {On Coxeter Arrangements and the Coxeter Number},
	volume = {8},
	doi = {10.2969/aspm/00810461},
	journal = {Advanced studies in pure mathematics},
	year = {1987},
	pages = {461--477}
}

@article{Molchanov,
	author = {Molchanov, V. F.},
	title = {Poincar{\'e} polynomials of representations of finite groups generated by reflections},
	volume = {31},
    number = {6},
	doi = {10.1007/BF01372350},
	journal = {Mathematical Notes of the Academy of Sciences of the USSR},
	year = {1982},
    month = jun,
	pages = {423--427}
}

@article{KamiyaTakemuraTeraoR,
	author = {Kamiya, H. and Takemura, A. and Terao, H.},
	title = {The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements},
	volume = {283},
	doi = {10.1007/978-3-0346-0209-9_7},
	journal = {Arrangements, Local Systems and Singularities. Progress in Mathematics},
	year = {2009},
	pages = {177--190}
}

@article{Littlewood,
	author = {Littlewood, D. E.},
	title = {Some Properties of $S$-Functions},
	volume = {s2-40},
    number = {1},
    doi = {10.1112/plms/s2-40.1.49},
	journal = {Proceedings of the London Mathematical Society},
	year = {1936},
	pages = {49--71}
}

@article{Haiman,
	author = {Haiman, M. D.},
	title = {Conjectures on the Quotient Ring by Diagonal Invariants},
	volume = {3},
    doi = {10.1023/A:1022450120589},
	journal = {Journal of Algebraic Combinatorics},
	year = {1994},
    month = jan,
	pages = {17--76}
}

@article{edelman1994free-mz,
	author = {Edelman, P. H.  and Reiner, V. },
	title = {Free hyperplane arrangements between {${A}_{n-1}$} and {${B}_{n}$}},
	volume = {215},
	number = {1},
	journal = {Mathematische Zeitschrift},
	year = {1994},
    doi = {10.1007/BF02571719}, 
	pages = {347--365}
}

@article{fulkerson1965incidence-pjom,
	author = {Fulkerson, D.  and Gross, O. },
	title = {Incidence matrices and interval graphs},
	volume = {15},
	number = {3},
	journal = {Pacific journal of mathematics},
	year = {1965},
    doi = {10.2140/PJM.1965.15.835},
	pages = {835--855}
}

@article{jambu1984free-aim,
	author = {Jambu, M.  and Terao, H. },
	title = {Free arrangements of hyperplanes and supersolvable lattices},
	volume = {52},
	doi = {10.1016/0001-8708(84)90024-0},
	number = {3},
	journal = {Advances in Mathematics},
	month = jun,
	year = {1984},
	pages = {248--258}
}

@book{orlik1992arrangements,
	author = {Orlik, P.  and Terao, H. },
	editor = {Artin, M.  and Chern, S. S.  and Coates, J.  and Fr{\"o}hlich, J. M.  and Hironaka, H.  and Hirzebruch, F.  and H{\"o}rmander, L.  and Moore, C. C.  and Moser, J. K.  and Nagata, M.  and Schmidt, W.  and Scott, D. S.  and Sinai, Y. G.  and Tits, J.  and Waldschmidt, M.  and Watanabe, S.  and Berger, M.  and Eckmann, B.  and Varadhan, S. R. S. },
	address = {Berlin, Heidelberg},
	series = {Grundlehren der mathematischen {Wissenschaften}},
	title = {Arrangements of {Hyperplanes}},
	volume = {300},
    doi = {10.1007/978-3-662-02772-1}, 
	publisher = {Springer Berlin Heidelberg},
	year = {1992}
}

@article{read1968introduction-joct,
	author = {Read, R. C. },
	title = {An introduction to chromatic polynomials},
	volume = {4},
	doi = {10.1016/S0021-9800(68)80087-0},
	number = {1},
	journal = {Journal of Combinatorial Theory},
	month = jan,
	year = {1968},
	pages = {52--71}
}

@article{suyama2019vertex-weighted-dcg,
	author = {Suyama, D.  and Tsujie, S. },
	title = {Vertex-{Weighted} {Graphs} and {Freeness} of {$ \psi $}-{Graphical} {Arrangements}},
	volume = {61},
	doi = {10.1007/s00454-018-9984-1},
	number = {1},
	journal = {Discrete \& Computational Geometry},
	month = jan,
	year = {2019},
	keywords = {52C35, 32S22, Chordal graph, Coxeter arrangement, Free arrangement, Hyperplane arrangement, Ish arrangement, Supersolvable arrangement, 05C15, 05C22, 13N15, 20F55, Graphical arrangement, Multiarrangement, Vertex-weighted graph},
	pages = {185--197}
}

@article{yoshinaga2007free-potjasams,
	author = {Yoshinaga, M. },
	title = {Free arrangements over finite field},
	volume = {82},
	doi = {10.3792/pjaa.82.179},
	number = {10},
	journal = {Proceedings of the Japan Academy, Series A, Mathematical Sciences},
	month = jan,
	year = {2007},
	keywords = {finitefiled, Free hyperplane arrangements},
	pages = {179--182}
}