Matroids Wk 1

Topics

• I’m self-learning Matroids over break. I am also sitting in occasionally on a class this upcoming Spring, but I won’t be able to make it for all, as I’m involved in a couple workshops and research that precludes my attending all (e.g. I’m out of town for three weeks so far for Spring).
• I’m following Oxley’s book, and watching the videos by Federico (currently on lecture 15). Primarily, once I get through the lectures (which should be in the next seven days or so), I can dig into the meat of the book. I started the book, to read concurrently, but it does take a lot longer to dig through, as it’s a lot denser to take in.
• I’ve also listed the papers I read this week related to that. The corrections are also really funny; my Notes app kept trying to correct “Gammoids” to be “Gammons” (apparently my OS is secretly an entity based in the UK with strong feelings on Brexit), so if you see weird stuff like that, please ignore it :)
• This week:
  • matroids and bases
  • Dependent vs Independent Sets (some recap from class)
  • laws of matroids, circuits,
  • Jordan Curve Thm
  • Circuit Elimination Axiom
  • Base Complement
  • Rank stuff (mostly recap from class)
  • Duality / Dual of Matroids
  • Kirchhoff’s Thm
  • Gammoids and strict Gammoids (co-transversal matroids) and submodularity

Reading Resources

• Whitney’s 1935 paper, “On the Abstract Properties of Linear Dependence”.
• “A non-constructive proof of the four colour theorem”
• “Counting rooted maps by genus I, II and III” (3 papers in all)
• “Gammoids and Transversal Matroids” by Ingleton and Piff
• Ardija’s “Traversal and cotransversal matroids via the Lindström lemma”
• Bruhn et al’s “Axioms for Infinite Matroids”

• JH Mason’s “On a Class of Matroids Arising from Paths in Graphs” (thanks for this, Graph Theory prof :)

• It’s Christmas, so just sneaking a bit of time before we start opening presents and all of that. I literally smell of dog right now, as one of them (aka the “trickster”) was licking my feet this morning, randomly, and nestling on my chest. Amazing.

And that’s it