Question

Bijective proof for the chromatic polynomial of a cycle

score 272 · Answer 1 · 2017-08-10 21:17:03

Bijective proof for the chromatic polynomial of a cycle

Published on 10 Aug 2017 - 21:17

score 142 · Answer 2 · 2017-08-11 20:26:59

How to prove this combinatorial identity $\sum^{m-1}_{k=0}\binom{n+m-1}{k} = \sum^{m-1}_{k=0}\binom{n+k-1}{k}\left(2^{m-k-1}\right)$?

score 117 · Answer 3 · 2017-08-12 00:43:44

117

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Combinatorial proof that two ways of counting are equal: $\sum_{r=2}^{n+1} \binom r2 = \binom{n+2}3$

Published on 12 Aug 2017 - 0:43

score 182 · Answer 4 · 2017-08-15 18:06:13

182

Views

Evaluating $\sum_{m=j_2-j}^{j_1} \frac{(j_1+m)!(j_2+j-m)!}{(j_1-m)!(j_2-j+m)!}$ using combinatorial identities

Published on 15 Aug 2017 - 18:06

score 91 · Answer 5 · 2017-08-17 11:45:57

91

Views

Number of $k-$subsets of $ \lbrace 1,2, \ldots ,n \rbrace$ with even sum.

Published on 17 Aug 2017 - 11:45

score 219 · Answer 6 · 2017-08-18 00:35:13

219

Views

What branch of math studies proving $g(\mathbf x) \leq g(\sigma \cdot \mathbf x)$ results?

Published on 18 Aug 2017 - 0:35

score 124 · Answer 7 · 2017-08-21 12:51:32

124

Views

Prove the identity $\frac{(2n)!}{2^n \cdot n!} = (2n-1)(2n-3)\cdots 3\cdot 1$ using combinatorial proof.

Published on 21 Aug 2017 - 12:51

score 9.7k · Answer 8 · 2017-08-27 10:54:49

In how many ways 5 different balls be distributed to 3 different boxes, when each box can hold any number of balls?

score 387 · Answer 9 · 2017-08-27 17:08:23

387

Views

A graph defined by a set of positive integers

Published on 27 Aug 2017 - 17:08

score 176 · Answer 10 · 2017-08-31 15:24:10

176

Views

Combinatorial proof of ${{n}\choose{4}}={{n-3}\choose{4}}+3{{n-3}\choose{3}}+3{{n-3}\choose{2}}+n-3$

Published on 31 Aug 2017 - 15:24

score 609 · Answer 11 · 2017-09-02 08:56:20

609

Views

Show that $ {2n \choose 3} - 2{n \choose 3} = n^2(n-1) $

Published on 02 Sep 2017 - 8:56

score 866 · Answer 12 · 2026-03-29 10:09:35

866

Views

How to write a proof: Catalan Numbers

Published on 29 Mar 2026 - 10:09

score 199 · Answer 13 · 2026-03-29 02:12:29

199

Views

Combinatorial interpretation of a sum with Stirling numbers

Published on 29 Mar 2026 - 2:12

score 161 · Answer 14 · 2017-09-14 04:40:34

161

Views

Combinatoric Proof of $\sum_0^n\binom{k-1+i}{k-1} = \binom{n+k}{k}$

Published on 14 Sep 2017 - 4:40

score 268 · Answer 15 · 2017-09-15 02:30:13

268

Views

Combinatorial proof of $\binom{k}{i}\binom{n}{k}=\binom{n}{i}\binom{n-i}{k-i}$

Published on 15 Sep 2017 - 2:30

List Question

Bijective proof for the chromatic polynomial of a cycle

How to prove this combinatorial identity $\sum^{m-1}_{k=0}\binom{n+m-1}{k} = \sum^{m-1}_{k=0}\binom{n+k-1}{k}\left(2^{m-k-1}\right)$?

Combinatorial proof that two ways of counting are equal: $\sum_{r=2}^{n+1} \binom r2 = \binom{n+2}3$

Evaluating $\sum_{m=j_2-j}^{j_1} \frac{(j_1+m)!(j_2+j-m)!}{(j_1-m)!(j_2-j+m)!}$ using combinatorial identities

Number of $k-$subsets of $ \lbrace 1,2, \ldots ,n \rbrace$ with even sum.

What branch of math studies proving $g(\mathbf x) \leq g(\sigma \cdot \mathbf x)$ results?

Prove the identity $\frac{(2n)!}{2^n \cdot n!} = (2n-1)(2n-3)\cdots 3\cdot 1$ using combinatorial proof.

In how many ways 5 different balls be distributed to 3 different boxes, when each box can hold any number of balls?

A graph defined by a set of positive integers

Combinatorial proof of ${{n}\choose{4}}={{n-3}\choose{4}}+3{{n-3}\choose{3}}+3{{n-3}\choose{2}}+n-3$

Show that $ {2n \choose 3} - 2{n \choose 3} = n^2(n-1) $

How to write a proof: Catalan Numbers

Combinatorial interpretation of a sum with Stirling numbers

Combinatoric Proof of $\sum_0^n\binom{k-1+i}{k-1} = \binom{n+k}{k}$

Combinatorial proof of $\binom{k}{i}\binom{n}{k}=\binom{n}{i}\binom{n-i}{k-i}$

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