List questions from combinatorial-proofs

Published on 29 Jan 2020 - 16:33

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Proving using a combinatorial argument?

Published on 31 Jan 2020 - 19:23

177

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Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

Published on 01 Feb 2020 - 17:23

564

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Simplify the expression $n + 2\binom{n}{2}$.

Published on 01 Feb 2020 - 18:08

284

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Combinatorial proof for Touchard's congruence

Published on 25 Mar 2026 - 11:14

201

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${n\choose 2} - {k\choose 2} = {n-k\choose 2} +k(n-k)$ Marked box or unmarked box

Published on 06 Feb 2020 - 2:38

51

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Combinatorial argument to prove counting.

Published on 09 Feb 2020 - 0:40

54

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An exact formula for counting solutions of the Frobenius equation summed to 8

Published on 10 Feb 2020 - 4:24

71

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Use of Bijection for computation

Published on 14 Feb 2020 - 21:42

114

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Showing that $\sum_{k=1}^n \binom nk 2^{n-k} = 3^n - 2^n$

Published on 18 Feb 2020 - 3:34

100

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Combinatorial proof using list counting

Published on 18 Feb 2020 - 20:57

68

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Prove a combinatorial identity with a combinatorial argument

Published on 19 Feb 2020 - 22:24

87

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How to prove a combinatorial identity with a combinatorial argument

Published on 20 Feb 2020 - 3:14

104

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Provide a combinatorial proof for an identity using the Binomial Theorem

Published on 21 Feb 2020 - 19:32

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Prove $\binom{n}{0} + \frac{1}{2} \binom{n}{1} + \frac{1}{3} \binom{n}{2} + ... + \frac{1}{n+1} \binom{n}{n} = \frac{2^{n + 1} - 1}{n + 1}$.

Published on 23 Feb 2020 - 21:48

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Formula for $\sum_{k=0}^n {n \choose k}^4$

Proving using a combinatorial argument?

Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

Simplify the expression $n + 2\binom{n}{2}$.

Combinatorial proof for Touchard's congruence

${n\choose 2} - {k\choose 2} = {n-k\choose 2} +k(n-k)$ Marked box or unmarked box

Combinatorial argument to prove counting.

An exact formula for counting solutions of the Frobenius equation summed to 8

Use of Bijection for computation

Showing that $\sum_{k=1}^n \binom nk 2^{n-k} = 3^n - 2^n$

Combinatorial proof using list counting

Prove a combinatorial identity with a combinatorial argument

How to prove a combinatorial identity with a combinatorial argument

Provide a combinatorial proof for an identity using the Binomial Theorem

Prove $\binom{n}{0} + \frac{1}{2} \binom{n}{1} + \frac{1}{3} \binom{n}{2} + ... + \frac{1}{n+1} \binom{n}{n} = \frac{2^{n + 1} - 1}{n + 1}$.

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