Lets Count Permutation Extrema! @DrWeselcouch

Lets Count Permutation Extrema! @DrWeselcouch

Uploaded August 2021 | Updated September 2026, 7 hours ago

We count the average number of local extrema in the permutations of 1, 2, ..., 2021.

Bonus question: What is the average number of local extrema in the permutations of 1, 2, ..., n?

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Lets Count Permutation Extrema!

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$Fractal Contest! VOTE! My students used Linear Algebra to generate these fractals. Comment your favorite. The one with the most votes gets EXTRA CREDIT! #Shorts Subscribe and Ring the 🔔 https://www.youtube.com/c/DrWeselcouch Reddit 👽 https://www.reddit.com/user/CoffeeAndCalcWithDrW PLAYLISTS 🎵 : Linear Algebra Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rfo0ifw9RZFoJ2Te2jk_pwX Number Theory Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfOeiBA6o4YSXtAWF3-3_AT Multivariable Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcdbQLLvRItUxOMRKnbDJaw Calculus 2 Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcqIZyidbChYLuMAdZhhEwN Math and Minecraft: https://youtube.com/playlist?list=PLscpLh9rN1Rf-dqLO4r3GAwvm1O_xL7D1 Combinatorics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfNzyUsA_KzsfQ_k1AR9Ebs Geometry Problems: https://youtube.com/playlist?list=PLscpLh9rN1RdFKjA3-vvTL_xG6s3YxB6r Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rcv3XYXq5Z0oXMEOVL-aocI Statistics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RexwCjV9_1RmfluCTv5HKe1$

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$It seems obvious, but how do you prove it? In this video we show that any n+1 element subset of {1, 2, ... , 2n} must have a pair of numbers where one divides the other. We prove this using the pigeonhole principle. Subscribe ✅ https://www.youtube.com/c/DrWeselcouch PLAYLISTS 🎵 : Number Theory Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfOeiBA6o4YSXtAWF3-3_AT Math and Minecraft: https://youtube.com/playlist?list=PLscpLh9rN1Rf-dqLO4r3GAwvm1O_xL7D1 Combinatorics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RfNzyUsA_KzsfQ_k1AR9Ebs Geometry Problems: https://youtube.com/playlist?list=PLscpLh9rN1RdFKjA3-vvTL_xG6s3YxB6r Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rcv3XYXq5Z0oXMEOVL-aocI Calculus 2 Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcqIZyidbChYLuMAdZhhEwN Multivariable Calculus Problems: https://youtube.com/playlist?list=PLscpLh9rN1RcdbQLLvRItUxOMRKnbDJaw Linear Algebra Problems: https://youtube.com/playlist?list=PLscpLh9rN1Rfo0ifw9RZFoJ2Te2jk_pwX Statistics Problems: https://youtube.com/playlist?list=PLscpLh9rN1RexwCjV9_1RmfluCTv5HKe1$

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Let's Count Permutation Extrema!