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International Conference on Finite Fields and Applications

Fq 2003: Finite Fields and Applications pp 109–136Cite as

Combinatorics of the Two-Variable Zeta Function

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Iwan M. Duursma

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  1. Iwan M. Duursma
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Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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Duursma, I.M. (2004). Combinatorics of the Two-Variable Zeta Function. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_9

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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