Combinatorics on words | Permutations | Enumerative combinatorics
In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation listed together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations. It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence in the OEIS). The first four smallest superpermutations have respective lengths 1, 3, 9, and 33, forming the strings 1, 121, 123121321, and 123412314231243121342132413214321. However, for n = 5, there are several smallest superpermutations having the length 153. One such superpermutation is shown below, while another of the same length can be obtained by switching all of the fours and fives in the second half of the string (after the bold 2): 123451234152341253412354123145231425314235142315423124531243512431524312543121345213425134215342135421324513241532413524132541321453214352143251432154321 For the cases of n > 5, a smallest superpermutation has not yet been proved nor a pattern to find them, but lower and upper bounds for them have been found. (Wikipedia).
If you rotate a bowling ball, it looks the same even though it's been "transformed". We say that the bowling ball exhibits "rotational symmetry". The particles making up the universe exhibit related kinds of symmetries, in which the particles are transformed but the equations describing th
From playlist Science Unplugged: Supersymmetry
In this video, Fermilab's Dr. Don Lincoln describes the principle of supersymmetry in an easy-to-understand way. A theory is supersymmetric if it treats forces and matter on an equal footing. While supersymmetry is an unproven idea, it is popular with particle physics researchers as a po
From playlist Speculative Physics
How do the additional symmetries of super-symmetry advance us toward a unified theory?
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From playlist Science Unplugged: Supersymmetry
The Universe is always surprising us with how little we know about... the Universe. It's continuously presenting us with stuff we never imagined, or even thought possible. The search for extrasolar planets is a great example. Since we started, astronomers have turned up over a thousand
From playlist Planets and Moons
AWESOME SUPERCONDUCTOR LEVITATION!!!
A quantum levitator it's a circular track of magnets above which a razor-thin disc magically levitates, seeming to defy the laws of physics. The key to the levitator is the disc, which is made of superconducting material sandwiched between layers of gold and sapphire crystal. A piece of fo
From playlist THERMODYNAMICS
Addendum for Supermasks in Superposition: A Closer Look (Paper Explained)
I take a closer look at "Supermasks in Superposition" after I've already done a video on it. Specifically, I look at: 1. The intuition and theoretical justification behind the G objective, 2. Whether Supermasks and Superposition can be viewed as two distinct ideas and 3. The Paper's Broade
From playlist Papers Explained
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MIT 8.04 Quantum Physics I, Spring 2016 View the complete course: http://ocw.mit.edu/8-04S16 Instructor: Barton Zwiebach License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 8.04 Quantum Physics I, Spring 2016
Light and Optics 7_6 More on Interference
The principle of linear superposition.
From playlist Physics - Light and Optics
Build Your Own Supercomputer 5 - Testing supercomputer process
Supercomputer Playlist: http://www.youtube.com/watch?v=13x90STvKnQ&list=PLQVvvaa0QuDf9IW-fe6No8SCw-aVnCfRi&feature=share In this part of how to build a supercomputer, we test the MPI and supercomputing technology on a single node. http://seaofbtc.com http://sentdex.com http://hkinsley.co
From playlist Build your Own Supercomputer
Is there any evidence that supersymmetry exists, or is it purely theoretical?
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From playlist Science Unplugged: Supersymmetry