Matroid Puns

Since the data is kind of messy an exact analytical solution is not ideal. I’m looking for n-best estimates of unique sets in a quasi n-nearest neighbors approach. And obviously most nearest neighbors algorithms I tried are not working.

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Hi all,

I recently stumbled across the theory of matroids. So far, I have only a very vague understanding of the topic and this questions is probably a very basic one. Is the entropy a matroid or a polymatroid? And what exactly is the difference between a matroid and a polymatroid? I found one paper where the authors argue, that the entropy is in general a polymatroid and becomes a matroid if the underlying random variables are independent and either uniform (entropy 1) or deterministic (entropy 0). I kind of don't understand where the entropy violates the definition of a proper matroid. Does someone have a good example maybe?

Thanks in advance! Any help appreciated :)

When will they be on the spirit board / shop? I have every single spirit except these.

Today's topic is Matroids.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week.

Experts in the topic are especially encouraged to contribute and participate in these threads.

These threads will be posted every Wednesday.

If you have any suggestions for a topic or you want to collaborate in some way in the upcoming threads, please send me a PM.

For previous week's "Everything about X" threads, check out the wiki link here

Next week's topics will be Symplectic geometry

I am dealing with some homeworks regarding matroids and their properties.

Yet, i am facing a new problem that i cannot fully grasp:

"What corresponds to one Base of the respective matroids?"

From my understanding, i thought the basis was the Set "S" and the conditions that of the subset "U".

These are already present, so i am not sure what is asked here.

Thank you in advance

Seriously, the fact that only two Matroids made it into Megaforce really saddens me. Which one do you think could have been best adapted?

View Poll

Hello, I'm writing my undergraduate thesis in mathematics. I study computer science but I love math so I picked Matroid Theory as a subject for my thesis. The goal is to present some equivalent definitions of matroids. Do you have any tips? My main concern is that it may get to be too long. You see I'm currently writing the introduction and I am planning to include basic notions of Relations over finite sets, Graph Theory, Linear algebra and traversal theory. I am trying to write a mathematical thesis to be both rigorous and easily understood by an undergraduate cs student.

tl;Dr Do you have any tips about how to balance writing a rigorous thesis and keeping it simple enough and self sufficient for a CS student to read (without writing a 10! - factorial of 10- pages text)

Hello Guys,

I would like to apologies first for my post being unstructured and grammatical errors and spelling mistakes.

So i have had a lecture about Matroids and it confuced me the crap out of me, because it is too abstract for me to grasp it. I have tried to research about it, but i feel like i am litterally to stupid to understand it.

So far, this is how far i can understand and not understand:

M = (S,I)

M is the Matroid, I asume its like a Tuple (because in my lecture notes it says 'ordered pair') that has elements from Set S

S is the "ground set" which is finite (for example number 1 to 10, Colours of the rainbow etc. )

I are the family of Subset of S (What does this even mean? Like multiple subsets that could have the same element in every set? Like for example:

S = {0, 1, 2, 3}

then

I = {{0} ,{1}, {2}, {3}, {1,2}, {0,1}, {1,3}, etc)

And there are those properties that the Matroids have:

• ∅ ∈ I
• A ⊂ B , B ∈ I so => A ∈ I
• ∀ A,B ∈ I with |B| = |A|+1, ∃ x ∈ B\A => A ∪ {x} ∈ I

The thinking errors i have is that i don't get the first property and how to know when the properties are not met, Like how do you find out how the "∅ ∈ I" when it is not defined so.

Any non-abstract examples are welcome.

Thank you in Advance

Hello everybody,

I posted this in r/math before but it was removed there (apologies for that). The suggestion was to post it here, so I copypasted it to here, hope that is permitted!

I'm currently reading up on Matroids which I, personally, find extremely interesting. I'm reading a paper about optimization on Matroids and their corresponding Polyhedra. Specifically, this paper makes use of an algorithm by Cunningham (1984): "Testing Membership in Matroid Polyhedra". The algorithm is also explained in Shrijvers excellent yet for an outsider hardcorely dense "Combanitorial Optimization: Polyhedra and Efficiency, Algorithms and Combinatorics, Vol. B", Theorem 40.4, but I find it extremely complicated to wrap my head around that stuff.

I know it is an extremely long shot, but I would honest-to-god like to understand how the Algorithm is supposed to work and how it optimizes. I tried looking for a matroid-related subreddit but unfortunately found none. If no one is capable (or willing) to engage with my oddly specific question, I absolutely understand.

Thanks and that's all, folks

I'm applying for a grant that would allow me to travel and attend a Matroid Theory conference (Oxley 65). This is my second quarter in my Master's program, and I'm pretty sure I would like to do my research on Matroid Theory, it is by far the most interesting field of math that I have encountered (besides combinatorics). In order to get the trip funded, I need to justify why I should go. I feel I personally have valid reasons

1. Well, as far as I know, it's really the only major matroid theory conference in the US.
2. It would be pretty fantastic to be able to meet so many other matroid theorists, learn what they are researching/have researched.
3. Network with other matroid theorists and learn about other applications/career opportunities exist for someone with a degree in matroid theory..
4. It generalizes and consolidates several aspects of graph theory and linear algebra, so I suppose I could pull in some of the beneficial aspects of those fields of study...

I just feel like I don't have any real heavy hitting reasons for a committee in charge of handing out grants to give me the grant to cover the travel expenses.. These few reasons mean a lot to me, but maybe not so much to the people reviewing the applications. I feel like if I knew some of the applications of matroid theory, I would feel more confident in my application. So my questions are, does anyone have any ideas of extra things I could put in my application to beef it up a bit?

• DOI/PMID/ISBN: 10.1016/j.aam.2019.101934

• URL

New; doesn't seem to be on Sci-Hub or LibGen, AFAICS

I live in Canada, and here I believe it comes in a 2 pack here. I'm wondering if I could order it by itself from another country.

EDIT: oh crap I spelt metroid wrong

In my class, we have defined the independent set axioms as:

(I1) \emptyset is independent

(I2) Every subset of an independent set is independent.

(I3) For each X \subseteq E(M), all maximal independent subsets of X have the same size.

My question is, for (I3), why must we consider all possible subsets X, and not just consider independent sets of E(M)? If they hold for the independent sets of E(M), doesn't it hold for all subsets of E(M)? My intuition is that if this was not the case, then say I and J are bases for some set X contained in E, with |I| > |J|, and all bases of M have the same cardinality. Then I and J span the same set, so any element in X U Y, for some Y in E\X, is not in the span of I if and only if it is not in the span of J, and thus, this would lead to an easy contradiction, by extending bases of I and J to bases of E.

Is there a hole in my logic? Thanks Reddit!

I am mainly a computer scientist, but I am rather theory-oriented. Linear algebra and graph theory are essential in CS and recently I learned about the existence of matroid theory, which generalizes some concepts of both. Could you recommend some readings to begin with? What are some important results/theorems?

Recently I have become obsessed with hypergraphs and possible generalizations of them. I've also read some articles on matroids in the context of hypergraphs. I've started to approach the limit on what I can find and would like a more rigorous treatment of the material. Can anyone recommend some books on the subjects?

In graphic matroids the circuits are called cycles but I am not sure what they are called when the matroid is algebraic. I also tried looking this up but couldn't find anything.

Hey guys, i have the following exercise to do:

================================ Let G= (V, E) be an undirected graph. Set M*k* (G) = (E, S) where

S = { A ⊆ E | A = F ∪ M where F is a forest and |M| ≤ k}

Prove that M*k*(G) is a matroid!

=================================

I don't understand the definition of S. What is the M? It can't be a matroid because I define A with A = F ∪ M. Is it an independence set?

Why is a uniform matroid with n elements and rank 2 called an n-point line?

Is there a good reason? Should it be obvious?