Paper Info
Title
The Partial-Fractions Method for Counting Solutions to Integral Linear Systems
Abstract
We present a new tool to compute the numberA(b) of integer solutions to the linear system x � 0 , A x = b , where the coefficients ofA and b are integral. �A(b) is often described as a vector partition function. Our methods use partial fraction expansions of Euler's generating function forA(b). A special class of vector partition functions are Ehrhart (quasi-)polynomials counting integer points in dilated polytopes. 1. Euler's generating function
Year
DOI
Venue
2004
10.1007/s00454-004-1131-5
Discrete & Computational Geometry
Keywords
Field
DocType
Vector partition function,Ehrhart theory,Littlewood-Richardson,Kostant partition function,BZ-triangles
Integer,Topology,Generating function,Combinatorics,Polynomial,Kostant partition function,Partition function (mathematics),Partition function (statistical mechanics),Polytope,Partial fraction decomposition,Mathematics
Journal
Volume
Issue
ISSN
32
4
Discrete & Computational Geometry 32 (2004), 437-446 (special issue in honor of Louis Billera)
Citations 
PageRank 
References 
3
0.51
10
Authors
1
Name
Order
Citations
PageRank
Matthias Beck15410.27