Matroid theory | Graph invariants | Computational problems | Polynomials | Duality theories
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph and contains information about how the graph is connected. It is denoted by . The importance of this polynomial stems from the information it contains about . Though originally studied in algebraic graph theory as a generalization of counting problems related to graph coloring and nowhere-zero flow, it contains several famous other specializations from other sciences such as the Jones polynomial from knot theory and the partition functions of the Potts model from statistical physics. It is also the source of several central computational problems in theoretical computer science. The Tutte polynomial has several equivalent definitions. It is equivalent to Whitney’s rank polynomial, Tutte’s own dichromatic polynomial and Fortuin–Kasteleyn’s random cluster model under simple transformations. It is essentially a generating function for the number of edge sets of a given size and connected components, with immediate generalizations to matroids. It is also the most general graph invariant that can be defined by a deletion–contraction recurrence. Several textbooks about graph theory and matroid theory devote entire chapters to it. (Wikipedia).
Learn how to write a polynomial in standard form and classify
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Lorenz: Hitler's "Unbreakable" Cipher Machine
Many people have heard of Enigma before, the code machine used by Nazi Germany to send secret coded messages. Yet, some very clever code breakers were able to break that code and read those messages! But there was another cipher machine used by the Germans in WWII called the Lorenz machin
From playlist My Maths Videos
Graph Convergence, Parameter Testing and Group Actions - Miklos Abert
Miklos Abert Alfred Renyi Institute of Mathematics, Budapest March 20, 2012 I will talk about two natural notions of convergence for sequences of graphs of bounded degree and their connection to groups and group actions. The first is Benjamini-Schramm convergence, which is strongly related
From playlist Mathematics
Bertrand Eynard - An overview of the topological recursion
The "topological recursion" defines a double family of "invariants" $W_{g,n}$ associated to a "spectral curve" (which we shall define). The invariants $W_{g,n}$ are meromorphic $n$-forms defined by a universal recursion relation on $|\chi|=2g-2+n$, the initial terms $W_{0,1}$
From playlist Physique mathématique des nombres de Hurwitz pour débutants
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Exploiting the Tiltman Break - Computerphile
Professor Brailsford returns to the subject of why Colossus was built. The professor's notes: http://www.eprg.org/computerphile/lorenz-combined.pdf Bletchley Park Playlist: https://www.youtube.com/playlist?list=PLzH6n4zXuckrSWWIDJ_3To7ro5-naSk8v Professor Brailsford used the book "C
From playlist Bletchley Park (Colossus) Playlist
Waht is SQL Injection | SQL Injection Tutorial | SQL Injection Tutorial for Beginners | Edureka
( PHP & MySQL with MVC Frameworks Certification Training - https://www.edureka.co/php-mysql-self-paced ) Watch Sample Class recording: http://www.edureka.co/php-mysql?utm_source=youtube&utm_medium=referral&utm_campaign=sql-injectn-tutt SQL injection is a code injection technique, used t
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Hibernate Tutorial | Hibernate Tutorial - 2 | Hibernate Tutorial for Beginners - 2 | Edureka
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From playlist Hibernate Tutorial Videos
Giancarlo Travaglini: Pick’s theorem and Riemann sums: a Fourier analytic tale
VIRTUAL LECTURE We show a connection between Fourier series and a celebrated theorem of G. Pick on the number of integer points in an integer polygon. Then we discuss an Euler-Maclaurin formula over polygons. Recording during the meeting "Discrepancy Theory and Applications" Find thi
From playlist Virtual Conference
Marie Albenque : Invariants de Tutte et convergence des cartes avec modèle d'Ising
Résumé : Angel and Schramm ont étudié en 2003 la limite locale des triangulations uniformes. La loi limite, appelée UIPT (pour Uniform Infinite planar Triangulation) a depuis été pas mal étudiée et est plutôt bien comprise. Dans cet exposé, je vais expliquer comment on peut obtenir un résu
From playlist Probability and Statistics
Sandro Franceschi : Méthode des invariants de Tutte et mouvement brownien réfléchi dans des cônes
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From playlist Probability and Statistics
Classify a polynomial and determine degree and Leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Jose Perea (5/2/21): Quasiperiodicity and Persistent Kunneth Theorems
A signal is said to be quasiperiodic if its constitutive frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window embedding of such a function can be shown to be dense in a torus of dimension equal to the number of independent frenquencies. I
From playlist TDA: Tutte Institute & Western University - 2021
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations