What is...Golomb-Dickman’s constant?
Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...Golomb-Dickman’s constant? Or: Cycles and primes.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...
Thumbnail.
Picture created using https://reference.wolfram.com/languag...
Main discussion.
Section 5.4 from https://vignette.wikia.nocookie.net/m... (this is Mathematical Constants – S.R. Finch)
https://en.wikipedia.org/wiki/Golomb%...
https://mathworld.wolfram.com/Golomb-...
https://golem.ph.utexas.edu/category/...
https://oeis.org/A084945
Background material.
https://en.wikipedia.org/wiki/Integer...
https://en.wikipedia.org/wiki/Prime_f...
https://en.wikipedia.org/wiki/Symmetr...
https://en.wikipedia.org/wiki/Permuta...
https://en.wikipedia.org/wiki/Random_...
https://en.wikipedia.org/wiki/Random_...
https://en.wikipedia.org/wiki/Cyclic_...
https://en.wikipedia.org/wiki/Number_...
https://en.wikipedia.org/wiki/Probabi...
https://en.wikipedia.org/wiki/Expecte...
https://en.wikipedia.org/wiki/Logarit...
Computer talk.
You can find the Mathematica notebook here: https://github.com/dtubbenhauer/My-Te...
Pictures used.
https://en.wikipedia.org/wiki/Integer...
Picture from • What is...the symmetric group?
A modification of a picture from • What is...the symmetric group?
Picture created using https://reference.wolfram.com/languag...
Another picture created using https://reference.wolfram.com/languag...
And another picture created using https://reference.wolfram.com/languag...
https://en.wikipedia.org/wiki/Prime_n...
YouTube and co.
• (Some) Algorithms for generating random pe...
• 27.3 Random Permutations
• S4:E5 Expected number of cycles in a rando...
#combinatorics
#numbertheory
#mathematics