Permutations | Factorial and binomial topics
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers less than or equal to n. Technically, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every element occurs exactly once as an image value. This is related to the rearrangement of the elements of S in which each element s is replaced by the corresponding f(s). For example, the permutation (3, 1, 2) mentioned above is described by the function defined as . The collection of all permutations of a set form a group called the symmetric group of the set. The group operation is the composition (performing two given rearrangements in succession), which results in another rearrangement. As properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set that are considered for studying permutations. In elementary combinatorics, the k-permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. When k is equal to the size of the set, these are the permutations of the set. (Wikipedia).
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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 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
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
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
Ex: Evaluate a Combination and a Permutation - (n,r)
This video explains how to evaluate a combination and a permutation with the same value of n and r. Site: http://mathispower4u.com
From playlist Permutations and Combinations
Ex: Evaluate a Combination and a Permutation - (n,1)
This video explains how to evaluate a combination and a permutation with the same value of n and r = 1. Site: http://mathispower4u.com
From playlist Permutations and Combinations
Mathilde Bouvel: Combinatorial specifications of permutation classes via their decomposition trees
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Combinatorics
CIRCULAR PERMUTATION | PERMUTATION SERIES | CREATA CLASSES
This is the 6th video under the PERMUTATION series. This video covers the concept of Circular Permutation in full detail using Animation & Visual Tools. Visit our website: https://creataclasses.com/ For a full-length course on PERMUTATION & COMBINATION: https://creataclasses.com/courses
From playlist PERMUTATION
L23.3 Permutation operators on N particles and transpositions
MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L23.3 Permutation operators on N particles and transpositions License: Cr
From playlist MIT 8.06 Quantum Physics III, Spring 2018
Limits of permutation sequences - Yoshi Kohayakawa
Conference on Graphs and Analysis Yoshi Kohayakawa June 5, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Mathilde Bouvel : Studying permutation classes using the substitution decomposition
Recording during the thematic meeting : "Pre-School on Combinatorics and Interactions" the January 09, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Combinatorics
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different
From playlist Visual Group Theory
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
Learning from ranks, learning to rank - Jean-Philippe Vert, Google Brain
Permutations and sorting operators are ubiquitous in data science, e.g., when one wants to analyze or predict preferences. As discrete combinatorial objects, permutations do not lend themselves easily to differential calculus, which underpins much of modern machine learning. In this talk I
From playlist Statistics and computation