Titlebook: Computing the Continuous Discretely; Integer-point Enumer Matthias Beck,Sinai Robins Textbook 20071st edition Springer-Verlag New York 2007

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A Discrete Version of Green’s Theorem Using Elliptic FunctionsWe now allow ourselves the luxury of using basic complex analysis. In particular, we assume that the reader is familiar with contour integration and the residue theorem. We may view the residue theorem as yet another result that intimately connects the continuous and the discrete: it transforms a continuous integral into a discrete sum of residues.

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0172-6056 in the real world. VIII Preface Indeed, the di?erence between the two realizations of volume can be thought of in physical terms as follows. On the one hand, the quant- level grid imposed by the molecular stru978-1-4419-2119-2978-0-387-46112-0Series ISSN 0172-6056 Series E-ISSN 2197-5604

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Textbook 20071st editione of P has the usual intuitive meaning of volume that we attach to everyday objects we see in the real world. VIII Preface Indeed, the di?erence between the two realizations of volume can be thought of in physical terms as follows. On the one hand, the quant- level grid imposed by the molecular stru

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Face Numbers and the Dehn—Sommerville Relations in Ehrhartian Terms which give linear relations among the face numbers .. They are called ., 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 (T

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https://doi.org/10.1007/978-1-349-13584-4licial groups are simplicial objects in a special theory . of cogroups. In this chapter we study the homotopy theory of “free” simplicial objects in any theory of cogroups, or more generally in any theory of coactions. Such homotopy theories are canonical generalizations of the homotopy theory of simplicial groups.