Harmonic Tutte polynomials of matroids
Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura
TL;DR
This paper introduces harmonic Tutte polynomials for matroids, generalizing Greene's theorem, and relates harmonic weight enumerators of codes to these polynomials.
Contribution
It presents the novel concept of harmonic Tutte polynomials and extends Greene's theorem to connect them with code weight enumerators.
Findings
Harmonic Tutte polynomials are defined for matroids.
A generalization of Greene's theorem is established.
Harmonic weight enumerators are expressed as evaluations of these polynomials.
Abstract
In the present paper, we introduce the concept of harmonic Tutte polynomials of matroids and discuss some of their properties. In particular, we generalize Greene's theorem, thereby expressing harmonic weight enumerators of codes as evaluations of harmonic Tutte polynomials.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Combinatorial Mathematics · graph theory and CDMA systems