๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Counting Lattice Points of Rational Polyhedra

โœ Scribed by Beifang Chen; Vladimir Turaev

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
153 KB
Volume
155
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.

โœฆ Synopsis

P : (n) x n: , where A is the set of all vertices of P and each P : (n) is a certain periodic function of n. The Ehrhart reciprocity law follows automatically from the above formula. We also present a formula for the coefficients of Ehrhart polynomials in terms of elementary symmetric functions. 2000 Academic Press L(P _ Q, n)=L(P, n)+L(Q, n)&L(P & Q, n).

๐Ÿ“œ SIMILAR VOLUMES

Minimally Distant Sets of Lattice Points
Minimally Distant Sets of Lattice Points
โœ Daniel J. Kleitman; Leornard J. Schulman ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 393 KB

We consider the problem of finding two sets of given cardinalities in certain grid graphs, so as to minimize the cross-distance between them. (This is the maximum Manhattan distance between points, one of the first set and another of the second set.) The question is answered completely for grids tha

Counting Pairs of Lattice Paths by Inter
Counting Pairs of Lattice Paths by Intersections
โœ Ira Gessel; Wayne Goddard; Walter Shur; Herbert S. Wilf; Lily Yen ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 377 KB

We count the pairs of walks between diagonally opposite corners of a given lattice rectangle by the number of points in which they intersect. We note that the number of such pairs with one intersection is twice the number with no intersection and we give a bijective proof of that fact. Some probabil