Question

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

score 59 · Answer 1 · 2026-04-13 23:19:52

59

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 13 Apr 2026 - 23:19

score 422 · Answer 2 · 2026-05-10 17:01:11

422

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

Published on 10 May 2026 - 17:01

score 196 · Answer 3 · 2026-04-16 08:01:12

196

Views

Words of weight 5 in in Ternary Golay Code

Published on 16 Apr 2026 - 8:01

score 82 · Answer 4 · 2026-04-08 05:22:12

82

Views

value of $k$ in binomial expression

Published on 08 Apr 2026 - 5:22

score 123 · Answer 5 · 2026-04-15 07:31:09

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 127 · Answer 6 · 2026-04-15 03:30:42

127

Views

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

Published on 15 Apr 2026 - 3:30

score 440 · Answer 7 · 2026-04-16 13:19:47

440

Views

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

Published on 16 Apr 2026 - 13:19

score 514 · Answer 8 · 2026-04-14 02:12:30

514

Views

Identity involving difference of binomial coefficients

Published on 14 Apr 2026 - 2:12

score 1.9k · Answer 9 · 2026-04-11 20:43:57

1.9k

Views

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

Published on 11 Apr 2026 - 20:43

score 197 · Answer 10 · 2026-04-15 03:14:12

197

Views

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

Published on 15 Apr 2026 - 3:14

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 276 · Answer 12 · 2026-04-12 10:45:59

276

Views

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

Published on 12 Apr 2026 - 10:45

score 476 · Answer 13 · 2026-04-16 04:16:47

476

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 16 Apr 2026 - 4:16

score 304 · Answer 14 · 2026-04-15 23:07:10

304

Views

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

Published on 15 Apr 2026 - 23:07

score 55 · Answer 15 · 2026-04-12 10:01:44

55

Views

Proving an Identity using Combinatorial Arguments

Published on 12 Apr 2026 - 10:01

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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