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- W2802501935 abstract "Let $V$ be a real vector space of dimension $n$ and let $Msubset V$ be a lattice. Let $Psubset V$ be an $n$-dimensional polytope with vertices in $M$, and let $varphicolon Vrightarrow CC $ be a homogeneous polynomial function of degree $d$ (i.e., an element of $Sym^{d} (V^{*})$). For $qin ZZ_{>0}$ and any face $F$ of $P$, let $D_{varphi ,F} (q)$ be the sum of $varphi$ over the lattice points in the dilate $qF$. We define a generating function $G_{varphi}(q,y) in QQ [q] [y]$ packaging together the various $D_{varphi ,F} (q)$, and show that it satisfies a functional equation that simultaneously generalizes Ehrhart--Macdonald reciprocity and the Dehn--Sommerville relations. When $P$ is a simple lattice polytope (i.e., each vertex meets $n$ edges), we show how $G_{varphi}$ can be computed using an analogue of Brion--Vergne's Euler--Maclaurin summation formula." @default.
- W2802501935 created "2018-05-17" @default.
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- W2802501935 date "2018-05-03" @default.
- W2802501935 modified "2023-09-24" @default.
- W2802501935 title "The Bott-Brion-Dehn-Ehrhart-Euler-Khovanskii-Maclaurin-Puhklikov-Sommerville-Vergne formula for simple lattice polytopes" @default.
- W2802501935 hasPublicationYear "2018" @default.
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