What are Stirling Numbers of the 1st Kind? [Discrete Mathematics]
This video introduces Stirling numbers of the 1st kind, with examples and a derivation of the recurrence relation for these numbers. We cover the algebraic and combinatorial definition of Stirling numbers of the 1st kind, using the coefficients of the rising/falling factorials and the properties of permutations and cycle notation for permutations. We cover some basic properties of Stirling numbers as well as compute some of them for ourselves using the recurrence relation. If you're interested in learning more, check out these links:
https://www.whitman.edu/mathematics/c...
https://en.wikipedia.org/wiki/Stirlin...
https://en.wikipedia.org/wiki/Permuta...
https://en.wikipedia.org/wiki/Cycles_...
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0:00 Definition
1:08 Example Table
1:55 Basic Properties
6:30 Recurrence Relation
9:55 Algebraic Viewpoint
12:55 Signed Stirling Numbers
14:45 Summary
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