Editing Ehrhart polynomial (section)

== Non-leading coefficient bounds ==
The polynomial's non-leading coefficients <math>c_0,\dots,c_{d-1}</math> in the representation 

:<math>L(P,t) = \sum_{r=0}^d c_r t^r</math> 

can be upper bounded:<ref>{{citation|last1=Betke|first1=Ulrich |last2=McMullen|first2=Peter|author2-link=Peter McMullen|date=1985-12-01|title=Lattice points in lattice polytopes| journal=[[Monatshefte für Mathematik]]| language=en|volume=99|issue=4|pages=253–265|doi=10.1007/BF01312545|s2cid=119545615 |issn=1436-5081}}</ref>

:<math>c_r \leq |s(d,r)| c_d + \frac{1}{(d-1)!} |s(d,r+1)|</math>

where <math>s(n,k)</math> is the [[Stirling numbers of the first kind|Stirling number of the first kind]]. Lower bounds also exist.<ref>{{citation|last1=Henk|first1=Martin|last2=Tagami|first2=Makoto|date=2009-01-01|title=Lower bounds on the coefficients of Ehrhart polynomials|journal=[[European Journal of Combinatorics]]|volume=30|issue=1|pages=70–83|doi=10.1016/j.ejc.2008.02.009|issn=0195-6698| arxiv=0710.2665|s2cid=3026293}}</ref>