In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle. Cycles are often denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted. For example, given X = {1, 2, 3, 4}, the permutation (1, 3, 2, 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 (so S = X) is a 4-cycle, and the permutation (1, 3, 2) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 (so S = {1, 2, 3} and 4 is a fixed element) is a 3-cycle. On the other hand, the permutation that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}. The set S is called the orbit of the cycle. Every permutation on finitely many elements can be decomposed into cycles on disjoint orbits. The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles, and denoted (1, 3) (2, 4). (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
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)
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 16 (permutations)
PERMUTATION | PERMUTATION SERIES | CREATA CLASSES
This is the 3rd video under the PERMUTATION series. This video covers the concept of Permutation in full detail using Animation & Visual Tools. Visit our website: https://creataclasses.com/ For a full-length course on PERMUTATION, COMBINATION & PROBABILITY: https://creataclasses.com/cou
From playlist PERMUTATION
PERMUTATION: CLUBBING OF ITEMS | PERMUTATION SERIES | CREATA CLASSES
This is the 5th video under the PERMUTATION series. This video covers the concept of Permutation of Clubbing of objects or items in full detail using Animation & Visual Tools. Visit our website: https://creataclasses.com/ For a full-length course on PERMUTATION, COMBINATION & PROBABILIT
From playlist PERMUTATION
Abstract Algebra - 5.1 Permutations, Composition, and Cycle Notation
In this video we will examine a permutation. We first look at array notation, then the function of composition. We finish by looking at both converting array notation to cycle notation and performing composition in cycle notation. * Note - your text covers cycle notation in the next subse
From playlist Abstract Algebra - Entire Course
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
Why There's 'No' Quintic Formula (proof without Galois theory)
Feel free to skip to 10:28 to see how to develop Vladimir Arnold's amazingly beautiful argument for the non-existence of a general algebraic formula for solving quintic equations! This result, known as the Abel-Ruffini theorem, is usually proved by Galois theory, which is hard and not very
From playlist Summer of Math Exposition Youtube Videos
Numberphile is also on Facebook: http://www.facebook.com/numberphile More links & stuff in full description below ↓↓↓ 142857 is the most "famous" of the intriguing cyclic numbers. Featuring Dr Tony Padilla from the University of Nottingham - https://twitter.com/DrTonyPadilla NUMBERPHILE
From playlist Tony Padilla on Numberphile
Joseph Landsberg: "Geometry associated to tensor network states"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "Geometry associated to tensor network states" Joseph Landsberg (Clay Scholar) - Texas A&M University - College Station Abstract: I will discuss geometric i
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Regular permutation groups and Cayley graphs
Cheryl Praeger (University of Western Australia). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 11. Abstract: Regular permutation groups are the 'smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as
From playlist PRIMA2009
Bettina EICK - Computational group theory, cohomology of groups and topological methods 1
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Legendrian Torus and Cable Links - Lisa Traynor
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Legendrian Torus and Cable Links Speaker: Lisa Traynor Affiliation: Bryn Mawr College Date: November 22, 2021 Legendrian torus knots were classified by Etnyre and Honda. I will explain the classification of Legendrian toru
From playlist Mathematics
Group theory 15:Groups of order 12
This lecture is part of an online mathematics course on group theory. It uses the Sylow theorems to classify the groups of order 12, and finds their subgroups.
From playlist Group theory
Visual Group Theory, Lecture 4.6: Automorphisms
Visual Group Theory, Lecture 4.6: Automorphisms An automorphism is an isomorphism from a group to itself. The set of all automorphisms of G forms a group under composition, denoted Aut(G). After a few simple examples, we learn how Aut(Z_n) is isomorphic to U(n), which is the group consist
From playlist Visual Group Theory
301.5D Cycle Notation for Permutations
How does cycle notation help express permutations? And, what do we learn about permutations from the process of diescovering their cycle notation?
From playlist Modern Algebra - Chapter 16 (permutations)
Frédéric de Portzamparc - Faiblesse structurelle des schémas McEliece avec clefs compactes
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From playlist Journées Codage et Cryptographie 2014
Jonathan Belcher: Bridge cohomology-a generalization of Hochschild and cyclic cohomologies
Talk by Jonathan Belcher in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-... on August 12, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)