Geodesic
A Combinatorial Reciprocity Theorem for Hyperplane Arrangements
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 3-10

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DOI

Given a nonnegative integer $m$ and a finite collection $A$ of linear forms on ${{\mathbb{Q}}^{d}}$ , the arrangement of affine hyperplanes in ${{\mathbb{Q}}^{d}}$ defined by the equations $\alpha \left( x \right)\,=\,k$ for $\alpha \,\in \,A$ and integers $k\,\in \,\left[ -m,\,m \right]$ is denoted by ${{A}^{m}}$ . It is proved that the coefficients of the characteristic polynomial of ${{A}^{m}}$ are quasi-polynomials in $m$ and that they satisfy a simple combinatorial reciprocity law.
DOI : 10.4153/CMB-2010-004-7
Mots-clés : 52C35, 05E99 
Athanasiadis, Christos A. A Combinatorial Reciprocity Theorem for Hyperplane Arrangements. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 3-10. doi: 10.4153/CMB-2010-004-7
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     author = {Athanasiadis, Christos A.},
     title = {A {Combinatorial} {Reciprocity} {Theorem} for {Hyperplane} {Arrangements}},
     journal = {Canadian mathematical bulletin},
     pages = {3--10},
     year = {2010},
     volume = {53},
     number = {1},
     doi = {10.4153/CMB-2010-004-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-004-7/}
}
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