Έλλεν Εμίλια Ά. Arson ζ.

Today I had realization.

Remember Remark 2.4. in https://codeberg.org/fogti/public-docs/raw/commit/86f7a49d02bb114cf175d99d7dea6e6f0c62d345b2256c1f965367a7077ac2cd/NWC-related/matroid-circuits/cxa-tiofam.pdf where I was unsure if that stuff also holds for the non-commutative case?

Well, by proposition 13 in https://www.sciencedirect.com/science/article/pii/S000187081400098X , we only need to deal with the direct sum of M with itself. And we can decompose instances of the NWC into their connected components, which means we can handle each part of the sum separately.

Thus it does hold for the non-commutative case (i.e. t=2,3 suffices) 🎉
#matroid

May 15 at 8:17pmWeb
Show threadΈλλεν Εμίλια Ά. Arson ζ.May 15
I think I should try to write a proper proof for the M+N \in TE(2) <=> M,N \in TE(2) which should follow directly from the interactions between the NWC and the connectivity relation.
Show threadΈλλεν Εμίλια Ά. Arson ζ.May 15
wait, by re-reading the paper I noticed I should actually focus on the Lemma 12 instead. That looks quite a but more difficult.