These days I have a chance to meet participants of the mathematical conference at the highest mountain of the Czech republic at one of the top CZ hotels. It inspires me to learn more about Matroid topics and draw the Great Bear Matroid / painted by myself in 2016/ in Python, as well. Matroids are frequently used in data classification, as well.
algebraic matroid - is self dual. A combinatorial structure, that expresses an abstraction of the relation of algebraic independence.
bipartite matroid - matroid all of whose circuits have even size. Is bipartite only if spectrum is symmetric.
bicircular matroid - bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent sets are the edge sets of pseudoforests of G, that is, the edge sets in which each connected component contains at most one cycle.
connected matroid - series of parallel network if it is binary and has no minor isomorhic wwith M(K4). cycle matroid - matroid whose elements are cycles is quite different from the better known “cycle matroid” of the matroid literature.
dual matroid - dual of a matroid M is another matroid M that has the same elements as M, and in which a set is independent if and only if M has a basis set disjoint from it.
eulerian matroid - when G is eulerian, its trail matroid has rank 1. A matroid whose elements can be partitioned into a collection of disjoint circuits. fano matroid - also called fano plane, is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. finite matroid - equivalent to geometric lattice. frame matroid - frame matroids linearly representable over finite fields. free matroid - the matroid in which the independent sets are all subsets of E. gammoid - matroid obtained by restricting strict gammoid to some subset. A matroid M is a strict gammoid only if its dual matroid M is transversal. identically self dual matroid - matroid is identically self-dual (ISD for short) when the set of bases is identical with the set of cobases.
isomorphic matroid - two matroids are isomorphic if there is a bijection from the ground set of one to the other such that a set is independent in the first matroid if and only if its image is independent in the second matroid. linear matroid - a linear matroid is a matroid that has a representation, and an F-linear matroid (for a field F) is a matroid that has a representation using a vector spaceover F.
matroid - in mathematics and combinatorics is matroid generalisation of linear independence in vector space. Usage: independent sets, bases, circuits, rank functions, closure operators, closed sets, flats. It comes from intersection of algebra and graph theory ( starting by 3 numbers each matroid is cycle matroid ).
paving matroid - paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. regular matroid - regular matroid is a matroid that can be represented over all fields. transversal matroid - are base orderable trail matroid - all the edges are distinct is a trail. If the vertices. uniform matroid - the independent sets are exactly the sets containing at most r elements, for some fixed integer r. An alternative definition is that every permutation of the elements is a symmetry. vamos matroid - the Vamos matroid has eight elements, which may be thought of as the eight vertices of a cube or cuboid. The matroid has rank 4: all sets of three or fewer elements are independent, and 65 of the 70 possible sets of four elements are also independent.
Refrences:
https://arxiv.org/pdf/1609.05574.pdf
https://www.sciencedirect.com/science/article/pii/S0195669884710341
https://github.com/matroid/matroid-python/blob/master/README.md
https://www.matroid.com
http://sv2-mat.ist.osaka-u.ac.jp/~higashitani/sano_slide.pdf
https://www.siue.edu/~aweyhau/teaching/seniorprojects/simpson_final.pdf
https://github.com/matroid/matroid-python
https://sharmaeklavya2.github.io/theoremdep/nodes/matroids/weights/greedy.html
https://doc.sagemath.org/html/en/reference/matroids/sage/matroids/advanced.html#module-sage.matroids.advanced
https://doc.sagemath.org/html/en/reference/matroids/py-modindex.html
https://www.sciencedirect.com/science/article/pii/S0195669884800190
https://en.wikipedia.org/wiki/Matroid
https://en.wikipedia.org/wiki/Dual_matroid
https://en.wikipedia.org/wiki/Vámos_matroid
https://en.wikipedia.org/wiki/Eulerian_matroid
https://en.wikipedia.org/wiki/Regular_matroid
https://en.wikipedia.org/wiki/Paving_matroid
https://en.wikipedia.org/wiki/Bipartite_graph
https://en.wikipedia.org/wiki/Hassler_Whitney
https://books.google.cz/books?id=QL2iYMBLpFwC&pg=PA222&redir_esc=y#v=onepage&q&f=false
https://www.cs.virginia.edu/~jlp/19.CYCLE.pdf
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