Editing Ehrhart polynomial (section)

==Generalizations==
It is possible to study the number of integer points in a polytope {{math|''P''}} if we dilate some facets of {{math|''P''}} but not others. In other words, one would like to know the number of integer points in semi-dilated polytopes. It turns out that such a counting function will be what is called a multivariate quasi-polynomial. An Ehrhart-type reciprocity theorem will also hold for such a counting function.<ref>{{citation| last=Beck |first= Matthias|title=Multidimensional Ehrhart reciprocity|journal=[[Journal of Combinatorial Theory]]|date=January 2002|volume=97|series=Series A| issue=1| pages=187–194| doi= 10.1006/jcta.2001.3220| arxiv= math/0111331|s2cid= 195227}}</ref>

Counting the number of integer points in semi-dilations of polytopes has applications<ref>{{citation| last=Lisonek| first=Petr| title= Combinatorial Families Enumerated by Quasi-polynomials|journal=[[Journal of Combinatorial Theory]]| year=2007| volume=114| series=Series A|issue=4|pages=619–630| doi=10.1016/j.jcta.2006.06.013| doi-access=free}}</ref> in enumerating the number of different dissections of regular polygons and the number of non-isomorphic unrestricted codes, a particular kind of code in the field of [[coding theory]].