List questions from combinatorial-proofs

Published on 04 Oct 2020 - 2:44

93

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What is the combinatorial interpretation behind the recursive relation: $L(n,k+1)=\frac{n-k}{k\left(k+1\right)}L(n,k)$

Published on 04 Oct 2020 - 5:08

165

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Using combinatorial argument to prove that ${ n\brack 3}=\frac{1}{2}\left(n-1\right)!\left[\left(H_{n-1}\right)^{2}-H_{n-1}^{\left(2\right)}\right]$

Published on 29 Mar 2026 - 18:36

77

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Combinatorial argument for identity with binomial coefficients

Published on 04 Oct 2020 - 16:43

91

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Binomial and combinatorics

Published on 07 Oct 2020 - 9:37

79

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If chess is deterministic, can we prove that from a set of infinitely large number of games, that white always wins/doesn't win?

Published on 08 Oct 2020 - 5:06

115

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combinatorial proof that $\sum_{i=0}^n {n+i\choose i}\frac{1}{2^i} = 2^n$

Published on 10 Oct 2020 - 21:19

185

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Recurrence formula of the MacMahon $q$-analog of the Catalan numbers

Published on 25 Mar 2026 - 19:10

104

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How do I prove ${\binom{n}{0}}+{\binom{n}{3}}+{\binom{n}{6}}+\cdots ={\frac{1}{3}}\left(2^{n}+2\cos {\frac{n\pi }{3}}\right)?$

Published on 26 Mar 2026 - 11:17

106

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Computation of the sum involving product of binomial coefficients

Published on 15 Oct 2020 - 17:36

152

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Linear map $\phi_d : Pol_d \to Pol_d$ in Beck-Robins' book.

Published on 16 Oct 2020 - 5:37

282

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Combinatorial Proof for Composite/Nested Binomial Coefficient

Published on 17 Oct 2020 - 5:32

351

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Sum of binomial coefficients $\binom{n-k}{k}$ and Fibonacci numbers

Published on 18 Oct 2020 - 10:34

548

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Lattice paths proof

Published on 20 Oct 2020 - 11:31

175

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How to prove $F_{n+1}^2 - F_{n-1}^2 = F_{2n} $ by combinatorial-proofs?

Published on 20 Oct 2020 - 19:44

List Question

Proving symmetry on a regular 2n-gon

What is the combinatorial interpretation behind the recursive relation: $L(n,k+1)=\frac{n-k}{k\left(k+1\right)}L(n,k)$

Using combinatorial argument to prove that ${ n\brack 3}=\frac{1}{2}\left(n-1\right)!\left[\left(H_{n-1}\right)^{2}-H_{n-1}^{\left(2\right)}\right]$

Combinatorial argument for identity with binomial coefficients

Binomial and combinatorics

If chess is deterministic, can we prove that from a set of infinitely large number of games, that white always wins/doesn't win?

combinatorial proof that $\sum_{i=0}^n {n+i\choose i}\frac{1}{2^i} = 2^n$

Recurrence formula of the MacMahon $q$-analog of the Catalan numbers

How do I prove ${\binom{n}{0}}+{\binom{n}{3}}+{\binom{n}{6}}+\cdots ={\frac{1}{3}}\left(2^{n}+2\cos {\frac{n\pi }{3}}\right)?$

Computation of the sum involving product of binomial coefficients

Linear map $\phi_d : Pol_d \to Pol_d$ in Beck-Robins' book.

Combinatorial Proof for Composite/Nested Binomial Coefficient

Sum of binomial coefficients $\binom{n-k}{k}$ and Fibonacci numbers

Lattice paths proof

How to prove $F_{n+1}^2 - F_{n-1}^2 = F_{2n} $ by combinatorial-proofs?

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