List questions from combinatorial-proofs

Published on 21 Feb 2014 - 21:42

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Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$

Published on 22 Feb 2014 - 22:46

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In the Proofs from the book; In praise of inequalities

Published on 09 Apr 2017 - 14:47

115

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Proving and generalizing a combinatorial identity

Published on 26 Mar 2026 - 14:17

379

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Prove using combinatorics $n \mid \binom{n}{m} \binom{n}{m-1}$

Published on 13 Apr 2017 - 19:09

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George Polya's theorem on the number of shortest routes on Pascal's Triangle

Published on 14 Apr 2017 - 7:33

713

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Prove that C(n, 2k)C(2k, k) = C(n, k)C(n − k, k), where n ≥ 2k > 0, by using (a) a combinatorial proof, (b) an algebraic proof

Published on 14 Apr 2017 - 20:59

166

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Rigorous Proof of $0!=1$

Published on 20 Apr 2017 - 1:49

141

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Understanding TDI proof using Cramer's rule (Giles and Pulleyblank)

Published on 30 Apr 2017 - 2:59

74

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How to prove that some combinatorical function has minimum on borders?

Published on 13 Jun 2017 - 5:27

166

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Combinatorics Proof for $\sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$

Published on 18 Jun 2017 - 17:06

165

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Combinatorial proof of Recurrence for the number of permutations of odd order

Published on 19 Jun 2017 - 4:48

972

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Stirling Number of the second kind recurrence combinatorial proof

Published on 29 Mar 2026 - 2:12

224

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Using complete graphs and a combinatorial proof, show $\sum_{i=1}^{j}$ ${k_i}\choose{2} $ $\leq$ ${n}\choose{2}$

Published on 26 Jul 2017 - 23:28

284

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A Curious binomial identity

Published on 07 Aug 2017 - 19:30

List Question

Combination proof $\sum_{k=1}^nk\binom{n}{k}^2=n\binom{2n-1}{n-1}$

Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$

In the Proofs from the book; In praise of inequalities

Proving and generalizing a combinatorial identity

Prove using combinatorics $n \mid \binom{n}{m} \binom{n}{m-1}$

George Polya's theorem on the number of shortest routes on Pascal's Triangle

Prove that C(n, 2k)C(2k, k) = C(n, k)C(n − k, k), where n ≥ 2k > 0, by using (a) a combinatorial proof, (b) an algebraic proof

Rigorous Proof of $0!=1$

Understanding TDI proof using Cramer's rule (Giles and Pulleyblank)

How to prove that some combinatorical function has minimum on borders?

Combinatorics Proof for $\sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$

Combinatorial proof of Recurrence for the number of permutations of odd order

Stirling Number of the second kind recurrence combinatorial proof

Using complete graphs and a combinatorial proof, show $\sum_{i=1}^{j}$ ${k_i}\choose{2} $ $\leq$ ${n}\choose{2}$

A Curious binomial identity

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