Order theory | Polytopes

Distributive polytope

In the geometry of convex polytopes, a distributive polytope is a convex polytope for which coordinatewise minima and maxima of pairs of points remain within the polytope. For example, this property is true of the unit cube, so the unit cube is a distributive polytope. It is called a distributive polytope because the coordinatewise minimum and coordinatewise maximum operations form the meet and join operations of a continuous distributive lattice on the points of the polytope. Every face of a distributive polytope is itself a distributive polytope. The distributive polytopes all of whose vertex coordinates are 0 or 1 are exactly the order polytopes. (Wikipedia).

Video thumbnail

Distributive Property

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply Polynomials

Video thumbnail

Introduction to the Distributive Property

This video explains the distributive property and provides examples on how to use the distributive property. http://mathispower4u.yolasite.com/

From playlist The Distributive Property and Simplifying Algebraic Expressions

Video thumbnail

Using the Box Method to Multiply a Trinomial by a Trinomial - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply a Trinomial by a Trinomial

Video thumbnail

using the distributive property to simplify mixed number calculations

Check out the main channel @polymathematic ! I absolutely hate mixed numbers, and given my preference, I would only every work with improper fractions. But even I have to admit that, under certain circumstances, simplifying with mixed numbers can be helpful. Subscribe: https://bit.ly/po

From playlist polymathematic #shorts

Video thumbnail

Easiest Way to Multiply Two Trinomials by Each Other - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply a Trinomial by a Trinomial

Video thumbnail

How To Multiply Using Foil - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply Polynomials

Video thumbnail

How to Multiply a Trinomial by a Trinomial Using Box Method - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply a Trinomial by a Trinomial

Video thumbnail

Why does the distributive property Where does it come from

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply Polynomials

Video thumbnail

How to Simplify an Expression Using Distributive Property - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply Polynomials

Video thumbnail

Guido Montúfar : Fisher information metric of the conditional probability politopes

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry

Video thumbnail

Lecture 1 | Random polytopes | Zakhar Kabluchko | EIMI

Online school "Randomness online" November 4 – 8, 2020 https://indico.eimi.ru/event/40/

From playlist Talks of Mathematics Münster's reseachers

Video thumbnail

Zakhar Kabluchko: Random Polytopes, Lecture III

In these three lectures we will provide an introduction to the subject of beta polytopes. These are random polytopes defined as convex hulls of i.i.d. samples from the beta density proportional to (1 − ∥x∥2)β on the d-dimensional unit ball. Similarly, beta’ polytopes are defined as convex

From playlist Workshop: High dimensional spatial random systems

Video thumbnail

Introduction to geometric invariant theory 2: Moment polytopes - Michael Walter

Optimization, Complexity and Invariant Theory Topic: Introduction to geometric invariant theory 2: Moment polytopes Speaker: Michael Walter Affiliation: University of Amsterdam Date: June 5. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Eliza O’Reilly: Facets of high dimensional random polytopes

We consider the model of n i.i.d. points chosen uniformly from the unit sphere in R^d and study the asymptotic behavior of the (d−1)-dimensional faces, or facets, of the convex hull of these points. In fixed dimension d, known asymptotic formulas as the number of points n grows provide res

From playlist Workshop: High dimensional spatial random systems

Video thumbnail

Rolf Schneider: Hyperplane tessellations in Euclidean and spherical spaces

Abstract: Random mosaics generated by stationary Poisson hyperplane processes in Euclidean space are a much studied object of Stochastic Geometry, and their typical cells or zero cells belong to the most prominent models of random polytopes. After a brief review, we turn to analogues in sp

From playlist Probability and Statistics

Video thumbnail

The matching polytope has exponential extension complexity - Thomas Rothvoss

Thomas Rothvoss University of Washington, Seattle March 17, 2014 A popular method in combinatorial optimization is to express polytopes P P , which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constrain

From playlist Mathematics

Video thumbnail

Zakhar Kabluchko: Random Polytopes II

In these three lectures we will provide an introduction to the subject of beta polytopes. These are random polytopes defined as convex hulls of i.i.d. samples from the beta density proportional to (1 − ∥x∥2)β on the d-dimensional unit ball. Similarly, beta’ polytopes are defined as convex

From playlist Workshop: High dimensional spatial random systems

Video thumbnail

Tensors: rank, entropy and entanglement - Matthias Christandl

Optimization, Complexity and Invariant Theory Topic: Tensors: rank, entropy and entanglement Speaker: Matthias Christandl Affiliation: University of Copenhagen Date: June 5. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Multiply a Trinomial by a Trinomial Using a Rectangle - Math Tutorial

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.

From playlist How to Multiply a Trinomial by a Trinomial

Related pages

Convex polytope | Stable matching polytope | Order polytope | Distributive lattice | Unit cube