For graphic and cographic matroids, the derivative g'_M(-1) equals (-1)^{c(M)-1} c(M), and computational data suggests many new properties of the coefficient N2.
Relations between M\"obius and coboundary polynomial
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$
For graphic and cographic matroids, the derivative g'_M(-1) equals (-1)^{c(M)-1} c(M), and computational data suggests many new properties of the coefficient N2.