Matroid theory

Binary matroid

In matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the matroids whose elements are the columns of a (0,1)-matrix and whose sets of elements are independent if and only if the corresponding columns are linearly independent in GF(2). (Wikipedia).

Video thumbnail

Solve a logarithmic equation with quadratic formula

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Solving a natural logarithmic equation using quadratic formula

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Anna De Mier: Approximating clutters with matroids

Abstract: There are several clutters (antichains of sets) that can be associated with a matroid, as the clutter of circuits, the clutter of bases or the clutter of hyperplanes. We study the following question: given an arbitrary clutter Λ, which are the matroidal clutters that are closest

From playlist Combinatorics

Video thumbnail

Solve Logarithmic Equations with Logs on Both Sides

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Using the equality of logarithms to solve an equation

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Using the equality of logarithms to solve an equation

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

The formal definition of a sequence.

We have an intuitive picture of sequences (infinite ordered lists). But there is a formal definition of sequences based out of the idea of a specific function between sets, specifically from the positive integers to the real numbers. ►Full DISCRETE MATH Course Playlist: https://www.youtu

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

Video thumbnail

Kevin Hendrey - Obstructions to bounded branch-depth in matroids (CMSA Combinatorics Seminar)

Kevin Hendrey (Institute for Basic Science) presents “Obstructions to bounded branch-depth in matroids”, 24 November 2020 (CMSA Combinatorics Seminar).

From playlist CMSA Combinatorics Seminar

Video thumbnail

Parametric Equations

Since we just covered polar equations, let's go over one other way we can graph functions. Parametric equations are actually a set of equations whereby two variables like x and y both depend on the same variable, usually time, and therefore each rectangular coordinate is determined by its

From playlist Mathematics (All Of It)

Video thumbnail

Joseph Bonin: Delta-matroids as subsystems of sequences of Higgs lifts

Abstract: Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which symmetric differences replace set differences. One way to get a delta-matroid is to t

From playlist Combinatorics

Video thumbnail

Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek

This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

Video thumbnail

Solving logarithmic equations

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Solving logarithmic equations with extraneous solution

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

Yusuke Kobayashi: A weighted linear matroid parity algorithm

The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so gener

From playlist Follow-Up-Workshop "Combinatorial Optimization"

Video thumbnail

Victor Chepoi: Simple connectivity, local to global, and matroids

Victor Chepoi: Simple connectivity, local-to-global, and matroids A basis graph of a matroid M is the graph G(M) having the bases of M as the vertex-set and the pairs of bases differing by an elementary exchange as edges. Basis graphs of matroids have been characterized by S.B. Maurer, J.

From playlist HIM Lectures 2015

Video thumbnail

Gyula Pap: Linear matroid matching in the oracle model

Gyula Pap: Linear matroid matching in the oracle model Linear matroid matching is understood as a special case of matroid matching when the matroid is given with a matrix representation. However, for certain examples of linear matroids, the matrix representation is not given, and actuall

From playlist HIM Lectures 2015

Video thumbnail

Zoltán Szigeti: Packing of arborescences with matroid constraints via matroid intersection

The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: Edmonds characterized digraphs having a packing of k spanning arborescences in terms of connectivity and later in terms of matroid intersection. D

From playlist Follow-Up-Workshop "Combinatorial Optimization"

Video thumbnail

Sahil Singla: Online Matroid Intersection Beating Half for Random Arrival

We study a variant of the online bipartite matching problem that we call the online matroid intersection problem. For two matroids M1 and M2 defined on the same ground set E, the problem is to design an algorithm that constructs the largest common independent set in an online fashion. At e

From playlist HIM Lectures 2015

Video thumbnail

Apply the equality of logarithms to solve, log2 (4x - 6) = log2 (2x + 8)

👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the equality sign as single terms. Then, we equate the numbe

From playlist Solve Logarithmic Equations with Logs on Both Sides

Video thumbnail

The log-concavity conjecture and the tropical Laplacian - June Huh

June Huh Princeton University; Veblen Fellow, School of Mathematics February 17, 2015 The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic g

From playlist Mathematics

Related pages

Geometric lattice | Finite field | Uniform matroid | Cactus graph | Graphic matroid | Fano plane | GF(2) | Eulerian matroid | Matroid | Disjoint union | Bipartite graph | Symmetric difference | Symmetric matrix | Matroid representation | Logical matrix | Matroid minor | Dual matroid | Regular matroid | Matroid oracle | Bipartite matroid