Combinatorics

Polynomial method in combinatorics

In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems. The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz, have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed. (Wikipedia).

Video thumbnail

How to use the zeros and multiplicity to graph the equation of a polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Graph the polynomial given polynomial and using multiplicity and end behavior

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Zeros, graphing, multiplicity polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Classify a polynomial then determining if it is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

C07 Homogeneous linear differential equations with constant coefficients

An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.

From playlist Differential Equations

Video thumbnail

Learn how to identify if a function is a polynomial and identify the degree and LC

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Determining if a function is a polynomial or not then determine degree and LC

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Find a Polynomial Function Given the Zeros, Multiplicity, and (0,a) (Degree 3)

This video explains how to determine the equation of a polynomial function in factored form from the zeros, multiplicity, and a the y-intercept. http://mathispower4u.com

From playlist Determining the Equations of Polynomial Functions

Video thumbnail

Graphing Cubic Functions

http://mathispower4u.wordpress.com/

From playlist Graphing Functions (Algebra 1)

Video thumbnail

1. A bridge between graph theory and additive combinatorics

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In an unsuccessful attempt to prove Fermat's last theorem

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

Video thumbnail

Additive Number Theory: Extremal Problems and the Combinatorics.... (Lecture 1) by M. Nathanson

Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod

From playlist Workshop on Additive Combinatorics 2020

Video thumbnail

Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek

Analysis & Mathematical Physics Topic: Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal Uncertainty Principle Speaker: Laura Cladek Affiliation: von Neumann Fellow, School Of Mathematics Date: December 14, 2022 We obtain new bounds on the additive energy

From playlist Mathematics

Video thumbnail

Alin Bostan: Computer algebra for lattice path combinatorics

Classifying lattice walks in restricted lattices is an important problem in enumerative combinatorics. Recently, computer algebra has been used to explore and to solve a number of difficult questions related to lattice walks. We give an overview of recent results on structural properties a

From playlist Combinatorics

Video thumbnail

Global symmetry from local information: The Graph Isomorphism Problem – László Babai – ICM2018

Combinatorics | Mathematical Aspects of Computer Science Invited Lecture 13.4 | 14.5 Global symmetry from local information: The Graph Isomorphism Problem László Babai Abstract: Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity stat

From playlist Combinatorics

Video thumbnail

Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018

Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

Video thumbnail

Unexpected Applications of Polynomials in Combinatorics - Larry Guth

Larry Guth Massachusetts Institute of Technology March 12, 2013 In 2007, Zeev Dvir shocked experts by giving a one-page proof of the finite field Kakeya problem. The new idea in the proof was to introduce high degree polynomials into a problem about points and lines. This idea has led to p

From playlist Mathematics

Video thumbnail

The Polynomial Method and Applications From Finite Field Kakeya to Distinct Distances - Larry Guth

Larry Guth University of Toronto; Member, School of Mathematics April 22, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Discrepancy of generalized polynomials by Anirban Mukhopadhyay

Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod

From playlist Workshop on Additive Combinatorics 2020

Video thumbnail

Determine if a Function is a Polynomial Function

This video explains how to determine if a function is a polynomial function. http://mathispower4u.com

From playlist Determining the Characteristics of Polynomial Functions

Video thumbnail

Optimization and Tropical Combinatorics (Lecture 1) by Michael Joswig

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

Related pages

Erdős distinct distances problem | Restricted sumset | Kakeya set | Cap set | Combinatorics | Szemerédi–Trotter theorem | Schwartz–Zippel lemma | Ham sandwich theorem | Homogeneous polynomial