In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates (labels) are the permutations of the first n natural numbers. The edges identify the shortest possible paths (sets of transpositions) that connect two vertices (permutations). Two permutations connected by an edge differ in only two places (one transposition), and the numbers on these places are neighbors (differ in value by 1). The image on the right shows the permutohedron of order 4, which is the truncated octahedron. Its vertices are the 24 permutations of (1, 2, 3, 4). Parallel edges have the same edge color. The 6 edge colors correspond to the 6 possible transpositions of 4 elements, i.e. they indicate in which two places the connected permutations differ. (E.g. red edges connect permutations that differ in the last two places.) (Wikipedia).
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
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From playlist Modern Algebra - Chapter 16 (permutations)
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
Permutation matrices | Lecture 9 | Matrix Algebra for Engineers
What is a permutation matrix? Define 2x2 and 3x3 permutation matrices. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jch
From playlist Matrix Algebra for Engineers
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3)
Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3) Licence: CC BY NC-ND 4.0Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perr
From playlist École d’été 2013 - Théorie des nombres et dynamique
Using the slope formula to determine if points make up a rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Quantum Geometry of Matroids by Dhruv Ranganathan
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)