List questions from combinatorial-proofs

Published on 19 Sep 2022 - 16:58

166

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Combinatorial proof of $\sum_{i=1}^{n} i^2$

Published on 24 Sep 2022 - 2:02

94

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Combinatorial and Algebraic Proof: $\binom{n}{2} - 1 = 2(n-2) +\binom{n-2}{2}$ where $n\geq2$

Published on 26 Sep 2022 - 16:34

19

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Combinatorial Proof for $\Sigma_{i=0}^r \binom{i + m -1}{m - 1} = \binom{m + r}{m}$ where $m\geq1$ and $r\geq0$

Published on 26 Sep 2022 - 17:28

60

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Validity of an Identity proven via combinatorial proof

Published on 26 Sep 2022 - 20:15

62

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A combinatorial proof revised

Published on 26 Sep 2022 - 23:50

48

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Make sure the combinatorial proof is correct

Published on 27 Sep 2022 - 3:50

56

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Sign of a permutation when two elements are removed

Published on 29 Sep 2022 - 14:31

71

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Combinatorial proof of $(k + 1)^{n} = \sum_{i=0}^{n} {n\choose i} k^{i}$

Published on 30 Sep 2022 - 0:50

65

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Combinatorial Proofs: Show that $\binom{n}{j+1}(j+1) = \binom{n}{n-j}(n-j)$

Published on 03 Oct 2022 - 0:07

56

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Combinatorial proof of an identity involving binomial coefficients $\sum_{k=3}^n {k \choose 3} = {n +1\choose4}$

Published on 03 Oct 2022 - 0:23

157

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$\binom{n+1}{2} + 2 \left ( \binom{2}{2} + \binom{3}{2} + \dots + \binom{n}{2} \right ) = 1^2+2^2+\dots+n^2.$

Published on 23 Feb 2026 - 12:33

149

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Find ordered pairs (x, y), such that |x-y| is divisible by 3

Published on 08 Oct 2022 - 14:43

62

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Finding RHS of combinatorial proof: $n^2=(n-2)^2+2(n-2)+2n$

Published on 11 Oct 2022 - 0:33

62

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Some combinatorial proofs using Principle of Inclusion and Exclusion

Published on 11 Oct 2022 - 6:42

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Extracting Coefficients of Generating Function

Combinatorial proof of $\sum_{i=1}^{n} i^2$

Combinatorial and Algebraic Proof: $\binom{n}{2} - 1 = 2(n-2) +\binom{n-2}{2}$ where $n\geq2$

Combinatorial Proof for $\Sigma_{i=0}^r \binom{i + m -1}{m - 1} = \binom{m + r}{m}$ where $m\geq1$ and $r\geq0$

Validity of an Identity proven via combinatorial proof

A combinatorial proof revised

Make sure the combinatorial proof is correct

Sign of a permutation when two elements are removed

Combinatorial proof of $(k + 1)^{n} = \sum_{i=0}^{n} {n\choose i} k^{i}$

Combinatorial Proofs: Show that $\binom{n}{j+1}(j+1) = \binom{n}{n-j}(n-j)$

Combinatorial proof of an identity involving binomial coefficients $\sum_{k=3}^n {k \choose 3} = {n +1\choose4}$

$\binom{n+1}{2} + 2 \left ( \binom{2}{2} + \binom{3}{2} + \dots + \binom{n}{2} \right ) = 1^2+2^2+\dots+n^2.$

Find ordered pairs (x, y), such that |x-y| is divisible by 3

Finding RHS of combinatorial proof: $n^2=(n-2)^2+2(n-2)+2n$

Some combinatorial proofs using Principle of Inclusion and Exclusion

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