List questions from combinatorial-proofs

149

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Given positive integers $n, k, i,$ prove $\binom{n}{k} = \sum_{j=i}^{n-k+i}\binom{j-i}{i-1}\binom{n-j}{k-i}$

Published on 18 May 2020 - 17:15

1k

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Combinatorial explanation of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$

Published on 19 May 2020 - 8:40

313

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Using 'tiling' proof technique to create combinatoric proofs about number relationships.

Published on 26 Mar 2026 - 12:52

47

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Prove combinatorially: $\sum_{r=0}^n (-1)^r \binom{n}{r}CC^{k-r}_n = 0$

Published on 23 May 2020 - 23:23

137

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Explain why $4$ cannot be replaced by $5$ in part a)

Published on 25 Mar 2026 - 10:52

184

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Combinatorial proof that $2^{n+1}-1=1+2+4+\dots+2^n$

Published on 27 May 2020 - 11:24

150

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Explain why the coefficient of $x^n$ in the Euler product is equal to the number of partitions of n?

Published on 25 Mar 2026 - 23:42

37

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Configuration of high-dimensional spheres

Published on 26 Mar 2026 - 4:32

47

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Prove the equation combinatorially [full answer provided] - I need explanation for the answer

Published on 31 May 2020 - 22:52

165

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Closed form for Lobb Numbers

Published on 08 Jun 2020 - 2:37

134

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Combinatorial Argument for a Binomial idenity

Published on 08 Jun 2020 - 11:12

126

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Combinatorial argument for the number of pairs whose sum is less than or equal to k

Published on 08 Jun 2020 - 22:38

69

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Dissecting a combinatorial proof

Published on 09 Jun 2020 - 0:08

816

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Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.

Published on 09 Jun 2020 - 20:39

69

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Combinatorial selection methodology

Published on 11 Jun 2020 - 17:08

List Question

Given positive integers $n, k, i,$ prove $\binom{n}{k} = \sum_{j=i}^{n-k+i}\binom{j-i}{i-1}\binom{n-j}{k-i}$

Combinatorial explanation of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$

Using 'tiling' proof technique to create combinatoric proofs about number relationships.

Prove combinatorially: $\sum_{r=0}^n (-1)^r \binom{n}{r}CC^{k-r}_n = 0$

Explain why $4$ cannot be replaced by $5$ in part a)

Combinatorial proof that $2^{n+1}-1=1+2+4+\dots+2^n$

Explain why the coefficient of $x^n$ in the Euler product is equal to the number of partitions of n?

Configuration of high-dimensional spheres

Prove the equation combinatorially [full answer provided] - I need explanation for the answer

Closed form for Lobb Numbers

Combinatorial Argument for a Binomial idenity

Combinatorial argument for the number of pairs whose sum is less than or equal to k

Dissecting a combinatorial proof

Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.

Combinatorial selection methodology

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