In order-theoretic mathematics, a graded partially ordered set is said to have the Sperner property (and hence is called a Sperner poset), if no antichain within it is larger than the largest rank level (one of the sets of elements of the same rank) in the poset. Since every rank level is itself an antichain, the Sperner property is equivalently the property that some rank level is a maximum antichain. The Sperner property and Sperner posets are named after Emanuel Sperner, who proved Sperner's theorem stating that the family of all subsets of a finite set (partially ordered by set inclusion) has this property. The lattice of partitions of a finite set typically lacks the Sperner property. (Wikipedia).
The Distributive Property (L2.4)
This video defines the distributive property and provides several examples of how to multiply using the distributive property. Video content created Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist The Distributive Property and Simplifying Algebraic Expressions
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
Extremal Combinatorics with Po-Shen Loh 04/01 Wed - 2
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Christian Gaetz: "Antichains and intervals in the weak order"
Asymptotic Algebraic Combinatorics 2020 "Antichains and intervals in the weak order" Christian Gaetz - Massachusetts Institute of Technology Abstract: The weak order is the partial order on the symmetric group S_n (or other Coxeter group) whose cover relations correspond to simple transp
From playlist Asymptotic Algebraic Combinatorics 2020
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
Easiest Way to Apply Distributive Property of a Monomial and a Binomial
👉 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
A beautiful combinatorical proof of the Brouwer Fixed Point Theorem - Via Sperner's Lemma
Using a simple combinatorical argument, we can prove an important theorem in topology without any sophisticated machinery. Brouwer's Fixed Point Theorem: Every continuous mapping f(p) from between closed balls of the same dimension have a fixed point where f(p)=p. Sperner's Lemma: Ever
From playlist Cool Math Series
👉 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
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
Topics in Combinatorics lecture 2.5 --- Sperner's theorem
How many subsets of {1,...,n} can you choose if no set in your collection is allowed to be a subset of another? An obvious construction is to take all sets of size n/2 (or (n-1)/2 if n is odd). Sperner's theorem tells us that this is the best we can do. It has a miraculously short and simp
From playlist Topics in Combinatorics (Cambridge Part III course)
How to Learn the Basics of The 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
Nevanlinna Prize Lecture: Equilibria and fixed points — Constantinos Daskalakis — ICM2018
Equilibria, fixed points, and computational complexity Constantinos Daskalakis Abstract: The concept of equilibrium, in its various forms, has played a central role in the development of Game Theory and Economics. The mathematical properties and computational complexity of equilibria are
From playlist Special / Prizes Lectures
Algorithmic Game Theory by Siddharth Barman
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
From playlist Summer Research Program On Dynamics Of Complex Systems 2019
How to Use the Distributive Property to Multiply Binomials - Polynomials
👉 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
Multiplying Two Binomials Together Using the 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 Polynomials
Henry Adams (9/3/20): Fair division
Title: Fair division Abstract: Suppose five roommates need to pay $3,000 dollars of rent per month for their five-bedroom apartment. The five bedrooms are not equivalent: one is bigger, one is smaller, one has more windows, one is closer to the kitchen, one is painted neon green. So it is
From playlist AATRN 2020
Multiplying Using the Difference of Two Squares - 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
How can you cut a square into equal triangles? | Nathan Dalaklis
You've read the title, it seems like a simple question, but an answer requires the p-adic norm, Sperner's lemma, and some more mathematical machinery. In this video, we give a proof of Sperner's lemma for the 2-dimensional case and introduce the p-adic norm in order to provide a proof for
From playlist The New CHALKboard
Extremal Combinatorics with Po-Shen Loh 04/03 Fri
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Using the Box Method to Multiply Two Binomials - 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