Question

Single Binomial Coefficient Sum in Two Free Variables

score 78 · Answer 1 · 2021-06-23 19:45:30

78

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Single Binomial Coefficient Sum in Two Free Variables

Published on 23 Jun 2021 - 19:45

score 48 · Answer 2 · 2021-06-24 01:28:31

48

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Combinatorial Proof of $\sum_{k=0}^m {m \choose k}{n \choose p+k}={m+n \choose m+p}$

Published on 24 Jun 2021 - 1:28

score 174 · Answer 3 · 2021-06-28 08:38:09

174

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Calculate closed form for summation involving binomial coefficients

Published on 28 Jun 2021 - 8:38

score 537 · Answer 4 · 2026-03-27 05:37:51

537

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How to Prove this Multiset Identity by Combinatorial Proof

Published on 27 Mar 2026 - 5:37

score 334 · Answer 5 · 2021-07-07 03:51:31

334

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How to prove this (seemingly elusive) double binomial identity?

Published on 07 Jul 2021 - 3:51

score 181 · Answer 6 · 2021-07-08 02:34:08

181

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Proof verification: Prove the combinatorial identity $\sum_{k=1}^{n}k\cdot {n\choose k}=n\cdot 2^{n-1} $

Published on 08 Jul 2021 - 2:34

score 115 · Answer 7 · 2021-07-13 16:35:28

115

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How do we prove that the probability remains the same?

Published on 13 Jul 2021 - 16:35

score 240 · Answer 8 · 2021-07-17 11:12:55

240

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Direct combinatorial proof that adding every other term in row of Pascal's triangle is $2^{n-1}$?

Published on 17 Jul 2021 - 11:12

score 222 · Answer 9 · 2021-07-18 20:57:14

222

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Direct combinatorial proof of three successive entries with ratio $3: 4: 5$ in Pascal's triangle?

Published on 18 Jul 2021 - 20:57

score 185 · Answer 10 · 2026-03-29 22:33:51

185

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Hint toward combinatorial proof of $\binom{n-1}{k}\binom{n}{k-1}\binom{n+1}{k+1} = \binom{n-1}{k-1}\binom{n}{k+1}\binom{n+1}{k}$

Published on 29 Mar 2026 - 22:33

score 63 · Answer 11 · 2021-07-25 11:58:13

63

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Proving $r \binom{n}{r}=\left( n-(r-1) \right) \binom{n}{r-1}$ using counting arguements

Published on 25 Jul 2021 - 11:58

score 235 · Answer 12 · 2021-07-26 09:32:30

235

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Combinatorial Proof for $\sum_{k=0}^n \binom{2n}{2k}^2 = \frac{1}{2}\left( \binom{4n}{2n}+(-1)^n \binom{2n}{n} \right)$

Published on 26 Jul 2021 - 9:32

score 94 · Answer 13 · 2026-03-27 03:44:25

94

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Combinatorial proof of this identity: $ \sum_{k=0}^m \left(\!\!\binom{n}k\!\!\right) = \left(\!\!\binom{n+1}m\!\!\right), n\geq0$

Published on 27 Mar 2026 - 3:44

score 79 · Answer 14 · 2026-03-27 07:28:14

79

Views

Proving combinatoric identity using vote casting example.

Published on 27 Mar 2026 - 7:28

score 187 · Answer 15 · 2026-03-29 21:37:41

187

Views

Combinatorics proof for number of paths starting from the origin and returning to the origin only at step $2n$.

Published on 29 Mar 2026 - 21:37

List Question

Single Binomial Coefficient Sum in Two Free Variables

Combinatorial Proof of $\sum_{k=0}^m {m \choose k}{n \choose p+k}={m+n \choose m+p}$

Calculate closed form for summation involving binomial coefficients

How to Prove this Multiset Identity by Combinatorial Proof

How to prove this (seemingly elusive) double binomial identity?

Proof verification: Prove the combinatorial identity $\sum_{k=1}^{n}k\cdot {n\choose k}=n\cdot 2^{n-1} $

How do we prove that the probability remains the same?

Direct combinatorial proof that adding every other term in row of Pascal's triangle is $2^{n-1}$?

Direct combinatorial proof of three successive entries with ratio $3: 4: 5$ in Pascal's triangle?

Hint toward combinatorial proof of $\binom{n-1}{k}\binom{n}{k-1}\binom{n+1}{k+1} = \binom{n-1}{k-1}\binom{n}{k+1}\binom{n+1}{k}$

Proving $r \binom{n}{r}=\left( n-(r-1) \right) \binom{n}{r-1}$ using counting arguements

Combinatorial Proof for $\sum_{k=0}^n \binom{2n}{2k}^2 = \frac{1}{2}\left( \binom{4n}{2n}+(-1)^n \binom{2n}{n} \right)$

Combinatorial proof of this identity: $ \sum_{k=0}^m \left(\!\!\binom{n}k\!\!\right) = \left(\!\!\binom{n+1}m\!\!\right), n\geq0$

Proving combinatoric identity using vote casting example.

Combinatorics proof for number of paths starting from the origin and returning to the origin only at step $2n$.

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