Lecture 8 - MULTISETS and MULTICHOOSE // Combinatorics Discrete Math

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We learn about multichoose and multisets in discrete mathematics with the standard stars and bars identification

0:00 What is an unordered list with repetitions?
0:31 Multisets and multiplicity
0:55 Notation, examples, and equality for multisets
2:10 Size of a multiset
2:45 Counting multisets using multichoose
3:47 2 Multichoose identities + a Combinatorial approach to a proof
7:19 stars and bars
  1. AfterMath
  2. multichoose
  3. multisets in discrete mathematics
  4. multisets
  5. math
  6. mathematics
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Комментарии
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Been looking to understand multisets after having read a textbook. Hearing this exposition has been most useful.

financialcafe
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GOD, that star and bar explanation made me amazed, Nice explanation

praveenkumarp
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Please start making videos again u r so great at explaining math concepts. ❤

adityanayak
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Multichoose sounds like you're just selecting with replacement, which is the same as treating your set as if each element in the set is infinite.

bodaciouschad
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there is a good application of this idea. if x + y + z = n, then # of points in 3d space satisfy this equation is 3+n-1 Choose n
here # of bars are 2 and stars are n, so, its basically ((3 multichoose n))

praveenkumarp