Question

Need help in following problems related to combinatorial analysis.

score 57 · Answer 1 · 2026-03-25 18:41:42

57

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Need help in following problems related to combinatorial analysis.

Published on 25 Mar 2026 - 18:41

score 733 · Answer 2 · 2015-11-10 18:18:02

733

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Prove combinatorial Identity using a combinatorial argument.

Published on 10 Nov 2015 - 18:18

score 890 · Answer 3 · 2015-11-17 11:49:11

890

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Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Published on 17 Nov 2015 - 11:49

score 201 · Answer 4 · 2015-12-03 20:26:40

201

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Prove this binomial identity using the following equality:

Published on 03 Dec 2015 - 20:26

score 161 · Answer 5 · 2026-03-24 15:03:34

161

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Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^3\binom{n}{k}=0$

Published on 24 Mar 2026 - 15:03

score 502 · Answer 6 · 2026-03-16 20:17:38

502

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

Published on 16 Mar 2026 - 20:17

score 482 · Answer 7 · 2026-03-25 16:17:14

482

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Combinatorial argument for an identity

Published on 25 Mar 2026 - 16:17

score 478 · Answer 8 · 2015-12-24 16:25:59

478

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closed form of $\sum_{k=0}^n {2n\choose 2k}2^k$

Published on 24 Dec 2015 - 16:25

score 143 · Answer 9 · 2015-12-24 17:42:44

143

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Calculating the value of $\lfloor(1+\sqrt{2})^{2n}\rfloor$

Published on 24 Dec 2015 - 17:42

score 652 · Answer 10 · 2016-01-05 22:05:00

652

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Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer

Published on 05 Jan 2016 - 22:05

score 1.8k · Answer 11 · 2016-01-11 14:28:09

1.8k

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What is a combinatorial proof exactly?

Published on 11 Jan 2016 - 14:28

score 98 · Answer 12 · 2026-03-26 01:28:31

98

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Isabelle and "Method of Coefficients"

Published on 26 Mar 2026 - 1:28

score 22.9k · Answer 13 · 2016-01-27 17:52:07

22.9k

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Show by combinatorial argument that ${2n\choose 2} = 2{n \choose 2} + n^2$

Published on 27 Jan 2016 - 17:52

score 805 · Answer 14 · 2016-02-04 02:07:27

805

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Seeking non-inductive, combinatorial proof of the identity $1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6}$

Published on 04 Feb 2016 - 2:07

score 684 · Answer 15 · 2016-02-05 06:35:45

684

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Proof with Combinatorial Argument $\sum_{i = 1}^{n} (i-1) = nC2$

Published on 05 Feb 2016 - 6:35

List Question

Need help in following problems related to combinatorial analysis.

Prove combinatorial Identity using a combinatorial argument.

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Prove this binomial identity using the following equality:

Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^3\binom{n}{k}=0$

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

Combinatorial argument for an identity

closed form of $\sum_{k=0}^n {2n\choose 2k}2^k$

Calculating the value of $\lfloor(1+\sqrt{2})^{2n}\rfloor$

Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer

What is a combinatorial proof exactly?

Isabelle and "Method of Coefficients"

Show by combinatorial argument that ${2n\choose 2} = 2{n \choose 2} + n^2$

Seeking non-inductive, combinatorial proof of the identity $1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6}$

Proof with Combinatorial Argument $\sum_{i = 1}^{n} (i-1) = nC2$

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