Relations between Möbius and coboundary polynomial

Details Relations between Möbius and coboundary polynomial Relations between Möbius and coboundary polynomial

2012-02-15

arxiv.org/abs/1202.3303v1

Mathematics

Combinatorics

12 pages

Scientific paper

It is known that, in general, the coboundary polynomial and the M\"obius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will try to answer if it is possible that the M\"obius polynomial of a matroid, together with the M\"obius 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.

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