List questions from combinatorial-proofs

Published on 09 May 2023 - 6:18

131

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Combinatorial interpretation of $\prod^\infty_{k=0}\left( 1+x^{2^k}\right) = \frac{1}{1-x}$

Published on 12 May 2023 - 7:45

83

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I need combinatorial proof for the following expression

Published on 15 May 2023 - 23:44

11

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Local h-polynomial with V=3.

Published on 26 Feb 2026 - 13:51

73

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Catalan number's combinatoric proof

Published on 16 May 2023 - 16:56

76

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Proving $\sum_{k=0}^{m}\binom{m}{k}\binom{n}{p+k}=\binom{m+n}{m+p}$ combinatorially

Published on 16 May 2023 - 21:10

79

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Problem with the proof of unordered sampling with replacement

Published on 26 Mar 2026 - 6:20

73

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Why is $\binom{k}{2}$ + $\binom{n−k}{2}$ maximized when $k = 1$ or $k = n - 1$?

Published on 22 May 2023 - 17:31

114

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Combinatorial argument for $\sum _{n=0}^\infty \binom{n}{k}y^n = \frac{y^k}{(1-y)^{k+1}}$

Published on 02 Jun 2023 - 14:58

104

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Inclusion-exclusion conundrum: $\sum_{k=1}^{\lfloor n/2\rfloor} (-1)^{k-1}k\binom{n-k}{k}2^{n-2k} = \binom{n+1}{3}$

Published on 04 Jun 2023 - 14:40

396

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Does this combinatorial identity hold？

Published on 05 Jun 2023 - 8:19

47

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How should I understand combinatorial proof?

Published on 06 Jun 2023 - 16:49

114

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Derivation for identities involving Stirling Numbers and Binomial Coefficients

Published on 10 Jun 2023 - 18:22

298

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I need the combinatorial proof for the following identity

Published on 11 Jun 2023 - 12:53

91

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Bijective proof for $\sum\limits_{\substack{n_1+n_2=n\\m_1+m_2=m}}\binom{n_1+m_1}{n_1}^2\binom{n_2+m_2}{n_2}^2=\frac{1}{2}\binom{2n+2m+2}{2n+1}$?

Published on 14 Jun 2023 - 10:34

List Question

Combinatorial proof of $\frac{(2n)!}{2^n \times n!} \in \mathbb{N}$

Combinatorial interpretation of $\prod^\infty_{k=0}\left( 1+x^{2^k}\right) = \frac{1}{1-x}$

I need combinatorial proof for the following expression

Local h-polynomial with V=3.

Catalan number's combinatoric proof

Proving $\sum_{k=0}^{m}\binom{m}{k}\binom{n}{p+k}=\binom{m+n}{m+p}$ combinatorially

Problem with the proof of unordered sampling with replacement

Why is $\binom{k}{2}$ + $\binom{n−k}{2}$ maximized when $k = 1$ or $k = n - 1$?

Combinatorial argument for $\sum _{n=0}^\infty \binom{n}{k}y^n = \frac{y^k}{(1-y)^{k+1}}$

Inclusion-exclusion conundrum: $\sum_{k=1}^{\lfloor n/2\rfloor} (-1)^{k-1}k\binom{n-k}{k}2^{n-2k} = \binom{n+1}{3}$

Does this combinatorial identity hold？

How should I understand combinatorial proof?

Derivation for identities involving Stirling Numbers and Binomial Coefficients

I need the combinatorial proof for the following identity

Bijective proof for $\sum\limits_{\substack{n_1+n_2=n\\m_1+m_2=m}}\binom{n_1+m_1}{n_1}^2\binom{n_2+m_2}{n_2}^2=\frac{1}{2}\binom{2n+2m+2}{2n+1}$?

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