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

Neat little set of experiments I did :)

https://harrison.totty.dev/p/positroid-structure-relu-networks

#mathematics #positroid #matroid

'Deletion Robust Non-Monotone Submodular Maximization over Matroids', by Paul Dütting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam.

http://jmlr.org/papers/v26/23-1219.html

#matroid #matroids #algorithms

Great introductory article on #matroid s:

Neel, David L., and Nancy Ann Neudauer. 2009. “Matroids You Have Known.” Mathematics Magazine 82 (1): 26–41. https://doi.org/10.1080/0025570X.2009.11953589.