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American Mathematical Monthly
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arXiv.org e-Print Archive
Preprint . 2008
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American Mathematical Monthly
Article . 2009 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2008
License: arXiv Non-Exclusive Distribution
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https://arxiv.org/pdf/0801.443...
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A Bijective Proof for a Theorem of Ehrhart

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Oct 2009Embargo end date: 01 Jan 2008 English Publisher:Informa UK LimitedJournal:American Mathematical Monthly, volume 116, pages 688-701 (issn: 0002-9890, eissn: 1930-0972, Copyright policy )
Authors: Steven V Sam;

doi: 10.4169/193009709x460813 , 10.48550/arxiv.0801.4432

arXiv: http://arxiv.org/abs/0801.4432

A Bijective Proof for a Theorem of Ehrhart

Abstract

We give a new proof for a theorem of Ehrhart regarding the quasi-polynomiality of the function that counts the number of integer points in the integral dilates of a rational polytope. The proof involves a geometric bijection, inclusion-exclusion, and recurrence relations, and we also prove Ehrhart reciprocity using these methods.

14 pages, 4 figures; v5: polished exposition, final version

Related Organizations
Keywords

05A15, 52C07, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Average
Average
Average
Green
bronze