Generalizations of Ehrhart-Macdonald reciprocity (Q2905221)

The author gives a new and purely combinatorial proof of the Ehrhart-Macdonald reciprocity theorem for arbitrary lattice invariant valuations. As in \textit{S. V. Sam}'s proof (see [Am. Math. Mon. 116, No. 8, 688--701 (2009; Zbl 1228.05065)]) the statement is first proved for simplices, but for the general case the author avoids triangulations. Instead he uses projections together with basic properties of the Euler characteristic. As a consequence, the author also re-proves Stanley's reciprocity theorem for generating functions with combinatorial methods.