Parity (mathematics) | Articles containing proofs | Permutations | Group theory
In mathematics, when X is a finite set with at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation of X can be defined as the parity of the number of inversions for σ, i.e., of pairs of elements x, y of X such that x < y and σ(x) > σ(y). The sign, signature, or signum of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd. The signature defines the alternating character of the symmetric group Sn. Another notation for the sign of a permutation is given by the more general Levi-Civita symbol (εσ), which is defined for all maps from X to X, and has value zero for non-bijective maps. The sign of a permutation can be explicitly expressed as sgn(σ) = (−1)N(σ) where N(σ) is the number of inversions in σ. Alternatively, the sign of a permutation σ can be defined from its decomposition into the product of transpositions as sgn(σ) = (−1)m where m is the number of transpositions in the decomposition. Although such a decomposition is not unique, the parity of the number of transpositions in all decompositions is the same, implying that the sign of a permutation is well-defined. (Wikipedia).
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
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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)
Statistics: Ch 8 Combinations and Permutations (1 of 22) What's the Difference?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between combinations and permutations. Combination: order DOES NOT matter. Permutation: order DOES matte
From playlist STATISTICS CH 8 COMBINATIONS AND PERMUTATIONS
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This video shows how to evaluate factorials, permutations, and combinations using a free online tool. https://oervm.s3-us-west-2.amazonaws.com/tvm/indexCP.html
From playlist Probability
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 16 (permutations)
Lec 22 | MIT 6.451 Principles of Digital Communication II
Lattice and Trellis Codes View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.451 Principles of Digital Communication II
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From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Complexity problems in enumerative combinatorics – Igor Pak – ICM2018
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From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Here I return to problem 52 after a comment from someone called Noam on the previous video in this series, who pointed out that I had made a mistake when claiming to have solved it. It wasn't immediately clear whether the mistake could be patched up somehow, but after a bit of thought I re
From playlist Thinking about maths problems in real time: mostly invariants problems
12. Solving problems with invariants -- one more problem
This question took me a long time, even though the eventual answer was an easy one-line proof. I'm not sure what I could have done to notice it more quickly, and unfortunately I'm also not really sure why the right idea suddenly came into my head. So it was an interesting experience but I
From playlist Thinking about maths problems in real time: mostly invariants problems
The PCP theorem, locally testable codes, and property testing - Irit Dinur
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This video explains how to determine the number of permutations when there are indistinguishable or repeated items. Site: http://mathispower4u.com
From playlist Permutations and Combinations
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RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures
From playlist Recent Developments in S-matrix Theory (Online)
Statistics: Ch 8 Combinations and Permutations (2 of 22) What 's the Difference?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will see an example of the difference between combinations and permutations from 5 numbers (pick any 3). Previous video in this s
From playlist STATISTICS CH 8 COMBINATIONS AND PERMUTATIONS
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I had a disaster for the first time since I've been doing this, which was to spend about an hour and a half recording a video, as I thought, only to discover that I had not pressed the record button. The selection this time turned out to consist of four problems that were uninteresting bec
From playlist Thinking about maths problems in real time: mostly invariants problems