Algebraic combinatorics | Theorems in combinatorics

Stanley's reciprocity theorem

In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior. (Wikipedia).

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Richard Taylor "Reciprocity Laws" [2012]

Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu

From playlist Number Theory

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Using the properties of rectangles to solve for x

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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Using the properties of a rectangle to find the missing value of an angle

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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What are the properties that make up a rectangle

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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Writing a two column proof using properties of rectangles for triangle congruence

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Number Theory | Quadratic Reciprocity

We prove the quadratic reciprocity theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Number Theory

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Xavier Viennot: Heaps and lattice paths

CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres MathΓ©matiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians

From playlist Combinatorics

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Given the properties of a rectangle determine the value of x

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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Writing a proof to prove a parallelogram is a rectangle

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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Circular Fence Posets and Associated Polytopes with Unexpected Symmetry by Mohan Ravichandran

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Christian Gaetz: "Antichains and intervals in the weak order"

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From playlist Asymptotic Algebraic Combinatorics 2020

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Determine the length of a diagonal of a rectangle

πŸ‘‰ Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are

From playlist Properties of Rectangles

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Stanley-Wilf limits are typically exponential - Jacob Fox

Jacob Fox Massachusetts Institute of Technology October 7, 2013 For a permutation p, let Sn(p) be the number of permutations on n letters avoiding p. Stanley and Wilf conjectured that, for each permutation p, Sn(p)1/n tends to a finite limit L(p). Marcus and Tardos proved the Stanley-Wilf

From playlist Mathematics

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Intrinsic mirror symmetry and categorical crepant resolutions - Daniel Pomerleano

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Intrinsic mirror symmetry and categorical crepant resolutions Speaker: Daniel Pomerleano Affiliation: University of Massachusetts, Boston Date: February 19, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Lecture 7: Compliance & Obedience || PSY 203: Social Psychology

This video series is for an online summer course in Social Psychology at Eureka College in Eureka, IL. It contains lecture material on a PowerPoint slideshow with me in the bottom right corner of the image. The episode/lecture discusses the following topics: compliance, foot in the door,

From playlist Social Psychology Lectures

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Stephen Roach: The Future of China

Mr. Roach has spent twenty-eight years in senior positions at Morgan Stanley β€” the bulk of that time as Chief Economist and more recently as Chairman of the firm's Asian businesses. In addition to his position at Yale, he remains the Non-Executive Chairman of Morgan Stanley Asia. Mr. Roa

From playlist The MacMillan Report

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Topics in Combinatorics lecture 7.4 --- The Marcus-Tardos theorem

We say that a permutation pi of {1,2,...,k} is contained in a permutation sigma of {1,2,...,n} if we can find k elements of {1,2,...,n} that are reordered by sigma in the way that pi reorders {1,2,...,k}. For instance, the permutation 2413 (meaning that 1 goes to 2, 2 goes to 4, 3 goes to

From playlist Topics in Combinatorics (Cambridge Part III course)

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Tony Bahri, Research talk - 10 February 2015

Tony Bahri (Rider University) - Research talk http://www.crm.sns.it/course/4350/ I shall describe geometric and algebraic approaches to the computation of the cohomology of polyhedral products arising from homotopy theory. A report on joint work with Martin Bendersky, Fred Cohen and Sam G

From playlist Algebraic topology, geometric and combinatorial group theory - 2015

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Alejandro Morales: "Asymptotics of principal evaluations of Schubert polynomials"

Asymptotic Algebraic Combinatorics 2020 "Asymptotics of principal evaluations of Schubert polynomials" Alejandro Morales - University of California, Los Angeles (UCLA) Abstract: Denote by u(n) the largest principal specialization of the Schubert polynomial of a permutation of size n. Sta

From playlist Asymptotic Algebraic Combinatorics 2020

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Discrete Math - 2.4.2 Recurrence Relations

What is a recurrence relation, and how can we write it as a closed function? Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

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Rational function | Convex polytope | Tuple | Functional equation | Mathematics | Combinatorics | Generating function | Ehrhart polynomial