Paper Info
Title
Combinatorics of the Two-Variable Zeta Function
Abstract
We consider the rank polynomial of a matroid and some well-known applications to graphs and linear codes. We compare rank polynomials with two-variable zeta functions for algebraic curves. This leads us to normalize the rank polynomial and to extend it to a rational rank function. As applications to linear codes we mention: A formulation of Greene's theorem similar to an identity for zeta functions of curves first found by Deninger, the definition of a class of generating functions for support weight enumerators, and a relation for algebraic-geometric codes between the matroid of a code and the two-variable zeta function of a curve.
Year
DOI
Venue
2003
10.1007/978-3-540-24633-6_9
CONTEMPORARY MATHEMATICS SERIES
Keywords
Field
DocType
zeta function,linear code,algebraic curve,generating function
Matroid,Discrete mathematics,Combinatorics,Riemann zeta function,Polynomial,Algebraic curve,Prime zeta function,Computer science,Arithmetic zeta function,Linear code,Rational function
Conference
Volume
ISSN
Citations 
2948
0302-9743
5
PageRank 
References 
Authors
0.58
12
1
Name
Order
Citations
PageRank
Iwan M. Duursma127926.85