List questions from combinatorial-proofs

Published on 14 Oct 2023 - 8:49

105

Views

Is there a combinatorial proof of this binomial-type formula involving Stirling numbers?

Published on 28 Mar 2026 - 0:00

84

Views

proof for $\sum_{r=0}^{40} {40 \choose r} (-1)^r {100-r \choose 40} = 1$

Published on 17 Oct 2023 - 8:51

76

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Prove that $\sum\limits_{i=0}^n(-1)^i\binom{n}{i}\binom{kn-ki}{n-1}=0$

Published on 19 Oct 2023 - 15:05

82

Views

How do I construct a bijection to prove the $q$-binomial theorem?

Published on 25 Mar 2026 - 12:46

78

Views

Understanding a proof on IMO shortlist 2016 C3

Published on 27 Mar 2026 - 21:34

48

Views

Sum involving Stirling numbers of the second kind and factorial

Published on 28 Mar 2026 - 0:00

69

Views

Central binomial coefficient identity

Published on 04 Nov 2023 - 18:18

88

Views

LYM inequality extension

Published on 08 Nov 2023 - 11:36

64

Views

algebraic or combinatorial proof to an identity of Stirling numbers of the first kind

Published on 28 Mar 2026 - 0:00

237

Views

Has this pattern in Pascal's triangle been already found?

Published on 11 Nov 2023 - 14:41

97

Views

Philip Hall's theorem

Published on 25 Mar 2026 - 17:26

26

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Bijective proof for Stirling numbers of the first kind

Published on 28 Mar 2026 - 0:00

80

Views

Proving that $ \beta(M) = \beta (M - e) + \beta (M /e).$

Published on 25 Mar 2026 - 17:26

75

Views

Symbolic method, bijective proofs or double counting proofs?

Published on 25 Mar 2026 - 4:37

List Question

Proving identities using combinatorial arguments

Is there a combinatorial proof of this binomial-type formula involving Stirling numbers?

proof for $\sum_{r=0}^{40} {40 \choose r} (-1)^r {100-r \choose 40} = 1$

Prove that $\sum\limits_{i=0}^n(-1)^i\binom{n}{i}\binom{kn-ki}{n-1}=0$

How do I construct a bijection to prove the $q$-binomial theorem?

Understanding a proof on IMO shortlist 2016 C3

Sum involving Stirling numbers of the second kind and factorial

Central binomial coefficient identity

LYM inequality extension

algebraic or combinatorial proof to an identity of Stirling numbers of the first kind

Has this pattern in Pascal's triangle been already found?

Philip Hall's theorem

Bijective proof for Stirling numbers of the first kind

Proving that $ \beta(M) = \beta (M - e) + \beta (M /e).$

Symbolic method, bijective proofs or double counting proofs?

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