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Combinatorics
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Stirling numbers
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Catalan numbers
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Counting Binary Ops (NRICH activity)
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Number of ways to triangulate a regular polygon
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Young tableau
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One Basket or Group Photo (NRICH activity)
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Combinatorial proof: Binomial theorem
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Double counting
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History of combinatorics
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Inclusion–exclusion principle
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Pigeonhole principle
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Picking socks in the dark
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Proving Vandermonde's identity
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Stars and bars
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Sum and product rules
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Sum of squares of binomial coefficients
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Bell numbers
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Combinatorics
Proving Vandermonde's identity
For \(0 \le m \le k \le n\), \(\displaystyle \binom{m + n}{k} = \sum_{j = 0}^k \binom{m}{j}\binom{n}{k - j}\)
70223
Discrete Mathematical Structures, Lecture 1.6: Combinatorial proofs
Professor Macauley
238
Vandemonde's Identity
Elliot Nicholson