List questions from combinatorial-proofs

692

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Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$

Published on 24 Mar 2017 - 22:27

245

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Prove statement using formulas and then using a counting argument.

Published on 01 Apr 2017 - 21:43

133

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Combinatorial proofs of the equation $\sum_{k=0}^{n} k{n \choose k}^2 = n {2n-1 \choose n-1}$

Published on 04 Apr 2017 - 23:42

66

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Combinatorial identities

Published on 08 Apr 2017 - 1:48

71

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Prove that $\Sigma_{i=0}^{n-1} (\Sigma_{j=i+1}^n(j(^nC_i) + i(^nC_j))) = n^22^{n-1}$

Published on 29 Jan 2023 - 9:04

85

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Consecutive Integer Sum of an m-member Sequence is Divisible by m Proof

Published on 30 Jan 2023 - 0:21

52

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Uniqueness of Radon point

Published on 31 Jan 2023 - 17:19

92

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lists with length $k$ with elements $b_1,b_2,\dots,b_k$ such that $|b_1|+|b_2|+···+|b_k| \le n$

Published on 01 Feb 2023 - 3:29

105

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Proving the Pigeonhole Principle: Strong Form

Published on 07 Feb 2023 - 20:06

145

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Combinatorics: A problem of 2 Discs

Published on 11 Feb 2023 - 2:59

82

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Applications of the pigeonhole principle (strong form)

Published on 13 Feb 2023 - 16:52

71

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average of pairs sitting next to each other - harder version

Published on 13 Feb 2023 - 22:05

131

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Probability Coin Toss Game Never Ties in N tosses

Published on 22 Feb 2023 - 21:44

115

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IMO Combinatorics C2 proof check

Published on 24 Feb 2023 - 17:08

77

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Proving $\sum_{1\le x\le y\le t}\frac{2^{t-x}}{xy}=\sum_{1\le x\le y\le t}\frac{C_t^0+C_t^1+\cdots+C_t^{y-1}}{xy}$ for positive integer $t$

Published on 26 Feb 2023 - 16:38

List Question

Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$

Prove statement using formulas and then using a counting argument.

Combinatorial proofs of the equation $\sum_{k=0}^{n} k{n \choose k}^2 = n {2n-1 \choose n-1}$

Combinatorial identities

Prove that $\Sigma_{i=0}^{n-1} (\Sigma_{j=i+1}^n(j(^nC_i) + i(^nC_j))) = n^22^{n-1}$

Consecutive Integer Sum of an m-member Sequence is Divisible by m Proof

Uniqueness of Radon point

lists with length $k$ with elements $b_1,b_2,\dots,b_k$ such that $|b_1|+|b_2|+···+|b_k| \le n$

Proving the Pigeonhole Principle: Strong Form

Combinatorics: A problem of 2 Discs

Applications of the pigeonhole principle (strong form)

average of pairs sitting next to each other - harder version

Probability Coin Toss Game Never Ties in N tosses

IMO Combinatorics C2 proof check

Proving $\sum_{1\le x\le y\le t}\frac{2^{t-x}}{xy}=\sum_{1\le x\le y\le t}\frac{C_t^0+C_t^1+\cdots+C_t^{y-1}}{xy}$ for positive integer $t$

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