Face Numbers and the Dehn—Sommerville Relations in Ehrhartian Terms
Our goal in this chapter is two fold, or rather, there is one goal in two different guises. The first one is to prove a set of fascinating identities, which give linear relations among the face numbers fk. They are called Dehn—Sommerville relations, in honor of their discoverers Max Wilhelm Dehn (1878–1952) and Duncan MacLaren Young Sommerville (1879–1934). Our second goal is to unify the Dehn—Sommerville relations (Theorem 5.1 below) with Ehrhart—Macdonald reciprocity (Theorem 4.1).
KeywordsFace Lattice Integer Point Face Number Ehrhart Polynomial Euler Relation
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