In combinatorial mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2, ..., k, k (with two copies of each value from 1 to k) with the additional property that, for each value i appearing in the permutation, the values between the two copies of i are larger than i. For instance, the 15 Stirling permutations of order three are 1,1,2,2,3,3; 1,2,2,1,3,3; 2,2,1,1,3,3;1,1,2,3,3,2; 1,2,2,3,3,1; 2,2,1,3,3,1;1,1,3,3,2,2; 1,2,3,3,2,1; 2,2,3,3,1,1;1,3,3,1,2,2; 1,3,3,2,2,1; 2,3,3,2,1,1;3,3,1,1,2,2; 3,3,1,2,2,1; 3,3,2,2,1,1. The number of Stirling permutations of order k is given by the double factorial (2k − 1)!!. Stirling permutations were introduced by in order to show that certain numbers (the numbers of Stirling permutations with a fixed number of descents) are non-negative. They chose the name because of a connection to certain polynomials defined from the Stirling numbers, which are in turn named after 18th-century Scottish mathematician James Stirling. Stirling permutations may be used to describe the sequences by which it is possible to construct a rooted plane tree with k edges by adding leaves one by one to the tree. For, if the edges are numbered by the order in which they were inserted, then the sequence of numbers in an Euler tour of the tree (formed by doubling the edges of the tree and traversing the children of each node in left to right order) is a Stirling permutation. Conversely every Stirling permutation describes a tree construction sequence, in which the next edge closer to the root from an edge labeled i is the one whose pair of values most closely surrounds the pair of i values in the permutation. Stirling permutations have been generalized to the permutations of a multiset with more than two copies of each value. Researchers have also studied the number of Stirling permutations that avoid certain patterns. (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 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
Maxim Kontsevich - Introduction to resurgence
I will explain the phenomenon of resurgence in a (apparently) new ex- ample related to Stirling formula, and its generalization to quantum dilogarithm. Let us define rational Stirling numbers (St_k) = (1, 1/12, 1/288, . . . ) as coeffi- cients in the asymptotic expansion of the normalized
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
Lecture 11 - Stirling & Harmonic Numbers
This is Lecture 11 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2011.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Introduction to Permutations and Combinations
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From playlist How to Calculate Permutations and Combinations
How to Calculate Permutations and Combinations from 5 Objects 3 at a time
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From playlist How to Calculate Permutations and Combinations
Are Stirling Engines the Future of Renewable Energy Storage?
Are Stirling Engines the Future of Renewable Energy Storage? Get Surfshark VPN at https://surfshark.deals/undecided and enter promo code UNDECIDED for 83% off and 3 extra months for free! Thanks to the rise of intermittent renewable energy sources, we’ve seen increased demand for new ene
From playlist The Future Of
Stanford Lecture: Donald Knuth—"Why Pi?"(2010)
Don Knuth's 16th Annual Christmas Tree Lecture December 6th, 2010 Professor Donald Knuth discusses recent discoveries that have uncovered a fascinating relationship between circles and the theory of trees. Learn more: http://scpd.stanford.edu/knuth/index.jsp
From playlist Donald Knuth Lectures
Stirling numbers and Pascal triangles | Wild Linear Algebra A 23 | NJ Wildberger
When we interpret polynomials as sequences rather than as functions, new bases become important. The falling and rising powers play an important role in analysing general sequences through forward and backward difference operators. The change from rising powers to ordinary powers, and fro
From playlist WildLinAlg: A geometric course in Linear Algebra
Stirling Engine Powered by Fresnel Lens/Concentrated Solar Power
This is my big Stirling engine being powered by my Fresnel lens, basically concentrated solar power or concentrated sunlight. I also used a mirror. I illustrate how the Fresnel lens concentrates the sunlight onto a mirror which reflects and continues the concentration onto the bottom of th
From playlist Science Projects
Best Stirling Engine Free Energy from the Sun EXPLAINED What is a Stirling Engine
Free solar energy from the sun and a large Fresnel lens is focused on the Stirling Engine displacer to produce flywheel movement. http://greenpowerscience.com/ Stirling Engines are heat engines that can operate from Solar concentrated sunlight. Robert Stirling invented the Stirling Engin
From playlist TV SHOW VIDEOS GREENPOWERSCIENCE.COM GREEN POWER SCIENCE
The Shadowy World of Umbral Calculus
An introduction to a famously enigmatic area of math, for calculus students of all levels ↓ Info and Timestamps ↓ In this video we use a primer on discrete calculus to motivate an exploration of the idea you saw in the thumbnail, deriving 2 summation methods along
From playlist Summer of Math Exposition 2 videos
Presenters: Itai Seggev & Devendra Kapadia Previously broadcast live on April 30, 2019 at twitch.tv/wolfram. For more information, please visit: https://www.wolfram.com/language/12/asymptotics/?product=language
From playlist Twitch Talks
This shows an interactive illustration that shows vector subtraction. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com.
From playlist Chapter 2 - Vectors
Free Power Stirling Engine TAKING ONE APART HOT AIR E Solar Power GreenPowerScience
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From playlist STIRLING CYCLE ENGINES HOT AIR ENGINES