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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2007). Face Numbers and the Dehn—Sommerville Relations in Ehrhartian Terms. In: Computing the Continuous Discretely. Springer, New York, NY. https://doi.org/10.1007/978-0-387-46112-0_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-46112-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-29139-0
Online ISBN: 978-0-387-46112-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)