List questions from combinatorial-proofs

Published on 25 Nov 2019 - 6:01

136

Views

Prove the following statement by combinatorial argument.

Published on 25 Nov 2019 - 7:59

266

Views

Prove that $\sum_{k=0}^{n} 2^{k} {n \choose k}{n-k \choose \lfloor{\frac{n-k}{2}}\rfloor} = {2n+1 \choose n}$

Published on 26 Nov 2019 - 14:43

347

Views

Two rooks shall attack each other on a chess board

Published on 26 Nov 2019 - 18:17

261

Views

Hypergeometric distribution question solving

Published on 30 Nov 2019 - 0:42

100

Views

Number of cover relations on partition

Published on 01 Dec 2019 - 16:37

173

Views

Prove prime $p$ divides $\binom{p^k}{n}$ for any $n$, $1 \le n \le p^k-1$, $k$ a positive integer

Published on 23 Feb 2026 - 5:45

106

Views

Proof for $\sum_{i=0}^n \frac{n \choose i}{{2n-1} \choose i} = 2$.

Published on 04 Dec 2019 - 19:00

522

Views

A combinatorial proof of the identity $\sum\limits_{k=0}^nk^2 {n \choose k}^2 = n^2 {2n - 2 \choose n- 1}$

Published on 07 Dec 2019 - 22:42

189

Views

Combinatorial proof of $\sum_{k=1}^n k^2{n\choose k}=n(n+1)2^{n-2}$

Published on 08 Dec 2019 - 19:13

82

Views

Combinatorial proof where n is an odd positive number and $n=2k+1$

Published on 09 Dec 2019 - 2:02

64

Views

A combinatorial interpretation for $n$-ary trees for negative $n$

Published on 10 Dec 2019 - 21:37

253

Views

Generalised Pascal Triangle with two-periodic formula

Published on 20 Dec 2019 - 7:03

106

Views

Combinatorial proof of $\binom{n+1}{k}=\frac{(n+1)\binom{n}{k-1}}{k}$

Published on 30 Dec 2019 - 12:22

134

Views

A collection of sets that cover all edges in Kn?

Published on 25 Mar 2026 - 11:06

List Question

Combinatorial proof using P.I.E

Prove the following statement by combinatorial argument.

Prove that $\sum_{k=0}^{n} 2^{k} {n \choose k}{n-k \choose \lfloor{\frac{n-k}{2}}\rfloor} = {2n+1 \choose n}$

Two rooks shall attack each other on a chess board

Hypergeometric distribution question solving

Number of cover relations on partition

Prove prime $p$ divides $\binom{p^k}{n}$ for any $n$, $1 \le n \le p^k-1$, $k$ a positive integer

Proof for $\sum_{i=0}^n \frac{n \choose i}{{2n-1} \choose i} = 2$.

A combinatorial proof of the identity $\sum\limits_{k=0}^nk^2 {n \choose k}^2 = n^2 {2n - 2 \choose n- 1}$

Combinatorial proof of $\sum_{k=1}^n k^2{n\choose k}=n(n+1)2^{n-2}$

Combinatorial proof where n is an odd positive number and $n=2k+1$

A combinatorial interpretation for $n$-ary trees for negative $n$

Generalised Pascal Triangle with two-periodic formula

Combinatorial proof of $\binom{n+1}{k}=\frac{(n+1)\binom{n}{k-1}}{k}$

A collection of sets that cover all edges in Kn?

Trending Questions

Popular # Hahtags

Popular Questions