Relations Between Möbius and Coboundary Polynomials
It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of the dual matroid, define the coboundary polynomial of the matroid. In some cases, the answer is affirmative, and we will give two constructions to determine the coboundary polynomial in these cases.
KeywordsMatroid theory Möbius polynomial Coboundary polynomial Coding theory
Mathematics Subject Classification (2010)05B35 11T71
The author would like to thank Ruud Pellikaan for stating the Main Question, and for valuable comments on this paper. The author is also indebted to an anonymous referee for the various comments on the paper and for the material in Sect. 6.
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