A closer look at lattice points in rational simplices (Q1307019)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A closer look at lattice points in rational simplices |
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A closer look at lattice points in rational simplices (English)
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16 January 2000
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The author obtains lattice point counting formulas for dilated rational \(n\)-dimensional polytopes showing that the number of lattice points in the interior of closure of a vector-dilated simplex are expressed by quasipolynomials that satisfy a general reciprocity law [see \textit{E. Ehrhart}, J. Reine Angew. Math. 227, 25-49 (1967; Zbl 0155.37503)]. As an example, a counting formula for a two-dimensional rectangular rational triangle is derived which permits the computation of the number of lattice points inside any rational polygon.
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lattice point
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\(n\)-dimensional polytopes
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simplex
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quasipolynomials
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