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Mathematics in Computer Science

, Volume 6, Issue 2, pp 121–133 | Cite as

Truncation Formulas for Invariant Polynomials of Matroids and Geometric Lattices

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Abstract

This paper considers the truncation of matroids and geometric lattices. It is shown that the truncated matroid of a representable matroid is again representable. Truncation formulas are given for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the truncation formula of the rank generating polynomial of a matroid by Britz.

Keywords

Matroid theory Geometric lattice Invariant polynomials 

Mathematics Subject Classification (2010)

05B35 
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Notes

Acknowledgments

We like to thanks the referees for the detailed remarks and the suggestion to give shorter proofs of the three main theorems.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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