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Ehrhart polynomial
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==The Betke–Kneser theorem== Ulrich Betke and [[Martin Kneser]]<ref>{{citation|last1=Betke|first1= Ulrich|last2= Kneser|first2=Martin|authorlink2=Martin Kneser| year=1985 | title=Zerlegungen und Bewertungen von Gitterpolytopen|journal= [[Crelle's Journal|Journal für die reine und angewandte Mathematik]] |volume=358|pages= 202–208|mr=0797683}}</ref> established the following characterization of the Ehrhart coefficients. A functional <math>Z</math> defined on integral polytopes is an <math>\operatorname{SL}(n,\Z)</math> and translation invariant [[Valuation (measure theory)|valuation]] if and only if there are real numbers <math>c_0,\ldots, c_n</math> such that :<math> Z= c_0 L_0+\cdots +c_n L_n.</math>
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