A combinatorial reciprocity theorem for hyperplane arrangements

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dc.creatorAthanasiadis, Christos A.
dc.date2006-10-16
dc.date.accessioned2026-07-07T07:29:07Z
dc.date.available2026-07-07T07:29:07Z
dc.descriptionGiven a nonnegative integer $m$ and a finite collection ${\mathcal A}$ of linear forms on ${\mathbb Q}^d$, the arrangement of affine hyperplanes in ${\mathbb Q}^d$ defined by the equations $α(x) = k$ for $α\in {\mathcal A}$ and integers $k \in [-m, m]$ is denoted by ${\mathcal A}^m$. It is proved that the coefficients of the characteristic polynomial of ${\mathcal A}^m$ are quasi-polynomials in $m$ and that they satisfy a simple combinatorial reciprocity law.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0610482
dc.identifierhttp://arxiv.org/abs/math/0610482
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117979
dc.subjectCombinatorics
dc.subject52C35
dc.titleA combinatorial reciprocity theorem for hyperplane arrangements
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