Question

Is it possible to show ${k\choose 2} \ge \sum_{i } {x_i\choose 2} $ such that $\sum_i x_i =k$

score 56 · Answer 1 · 2018-11-18 09:46:51

56

Views

Is it possible to show ${k\choose 2} \ge \sum_{i } {x_i\choose 2} $ such that $\sum_i x_i =k$

Published on 18 Nov 2018 - 9:46

score 419 · Answer 2 · 2026-03-25 06:06:28

419

Views

Is there a combinatorial proof that the Catalan number $C_n$ satisfies $(n+1)C_n={2n \choose n}$?

Published on 25 Mar 2026 - 6:06

score 193 · Answer 3 · 2018-12-04 12:42:29

193

Views

Words of weight 5 in in Ternary Golay Code

Published on 04 Dec 2018 - 12:42

score 80 · Answer 4 · 2018-12-06 06:40:56

80

Views

value of $k$ in binomial expression

Published on 06 Dec 2018 - 6:40

score 122 · Answer 5 · 2026-03-25 16:46:26

Pigeonhole Principle: Proof that in an isosceles triangle with both side lengths 2 amongst 5 random points within there's two with distance $d < 1$

score 125 · Answer 6 · 2018-12-08 16:37:18

125

Views

Proving $\binom{n+1+m}{n+1}=\sum_{k=0}^m(k+1)\binom{n+m-k}{n}$

Published on 08 Dec 2018 - 16:37

score 437 · Answer 7 · 2018-12-19 06:39:55

437

Views

Combinatorial proof that the number of even cardinality subsets is equal to the number of odd cardinality subsets

Published on 19 Dec 2018 - 6:39

score 511 · Answer 8 · 2018-12-22 15:50:31

511

Views

Identity involving difference of binomial coefficients

Published on 22 Dec 2018 - 15:50

score 1.9k · Answer 9 · 2026-03-25 07:43:50

1.9k

Views

Catalan numbers: bijection between applications of a binary operator and Dyck words.

Published on 25 Mar 2026 - 7:43

score 195 · Answer 10 · 2026-03-25 17:24:29

195

Views

Combinatorial Proof that $p(n)/(1+\epsilon)^n \to 0$

Published on 25 Mar 2026 - 17:24

score 60 · Answer 11 · 2026-03-25 13:55:38

60

Views

How to make any natural numbers (placed in the chessboard cells) divisible by 10 by using the given tools

Published on 25 Mar 2026 - 13:55

score 273 · Answer 12 · 2019-01-15 18:36:11

273

Views

Binomial sum which adds to $2^n n!$

Published on 15 Jan 2019 - 18:36

score 473 · Answer 13 · 2019-01-17 14:50:41

473

Views

How to show $n=1+\sum_{k=1}^{n}\left\lfloor{\log_2\frac{2n-1}{2k-1}}\right\rfloor$ for every natural number $n$.

Published on 17 Jan 2019 - 14:50

score 301 · Answer 14 · 2019-01-18 15:24:52

301

Views

Evaluate $4^n = \sum_{k=0}^{n} {n \choose k} 3^k$

Published on 18 Jan 2019 - 15:24

score 52 · Answer 15 · 2019-01-21 01:30:37

52

Views

Proving an Identity using Combinatorial Arguments

Published on 21 Jan 2019 - 1:30

List Question

Is it possible to show ${k\choose 2} \ge \sum_{i } {x_i\choose 2} $ such that $\sum_i x_i =k$

Is there a combinatorial proof that the Catalan number $C_n$ satisfies $(n+1)C_n={2n \choose n}$?

Words of weight 5 in in Ternary Golay Code

value of $k$ in binomial expression

Pigeonhole Principle: Proof that in an isosceles triangle with both side lengths 2 amongst 5 random points within there's two with distance $d < 1$

Proving $\binom{n+1+m}{n+1}=\sum_{k=0}^m(k+1)\binom{n+m-k}{n}$

Combinatorial proof that the number of even cardinality subsets is equal to the number of odd cardinality subsets

Identity involving difference of binomial coefficients

Catalan numbers: bijection between applications of a binary operator and Dyck words.

Combinatorial Proof that $p(n)/(1+\epsilon)^n \to 0$

How to make any natural numbers (placed in the chessboard cells) divisible by 10 by using the given tools

Binomial sum which adds to $2^n n!$

How to show $n=1+\sum_{k=1}^{n}\left\lfloor{\log_2\frac{2n-1}{2k-1}}\right\rfloor$ for every natural number $n$.

Evaluate $4^n = \sum_{k=0}^{n} {n \choose k} 3^k$

Proving an Identity using Combinatorial Arguments

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