Question

Does this equation hold in general?

score 546 · Answer 1 · 2019-07-09 11:26:14

546

Views

Does this equation hold in general?

Published on 09 Jul 2019 - 11:26

score 129 · Answer 2 · 2019-07-09 16:58:21

129

Views

Does this identity with binomial coefficients have a combinatorial interpretation?

Published on 09 Jul 2019 - 16:58

score 168 · Answer 3 · 2019-07-12 01:59:11

168

Views

Uniformly Distributed Random-Variable With Specific Ordering

Published on 12 Jul 2019 - 1:59

score 40 · Answer 4 · 2019-07-12 07:19:19

40

Views

Can a upper bound of $\sum_{b=1}^{p-1}\left(\frac{b^2-a^2}{p}\right)\left(\frac{b^2-1}{p}\right)$, $a\in{Z}$, be strictly less than $\sqrt{p}$?

Published on 12 Jul 2019 - 7:19

score 579 · Answer 5 · 2019-07-17 19:19:49

579

Views

Combinatorial proof of $\sum_{k=0}^{n} \binom{3n-k}{2n} = \binom{3n+1}{n}$

Published on 17 Jul 2019 - 19:19

score 83 · Answer 6 · 2019-07-19 07:02:16

83

Views

If $a_1 + a_2 + \dots + a_{100}=0$, with $a_1,\dots,a_{100}\in\mathbb{R}$, prove that $a_i+a_j \geq0, i\neq j,$ for at least $99$ $i,j$-pairs

Published on 19 Jul 2019 - 7:02

score 71 · Answer 7 · 2019-08-01 21:07:58

71

Views

Let, there be a matrix of order $N$ with all distinct entries. Using the given entries, is the sum of determinants of all possible matrices zero?

Published on 01 Aug 2019 - 21:07

score 939 · Answer 8 · 2026-03-25 10:55:46

939

Views

Bijection between Dyck paths with $k$ peaks and $n+1-k$ peaks

Published on 25 Mar 2026 - 10:55

score 51 · Answer 9 · 2019-08-20 12:19:58

51

Views

Throwing a die three times - check my proof

Published on 20 Aug 2019 - 12:19

score 493 · Answer 10 · 2026-03-25 12:45:34

493

Views

Equality like Pascal triangle

Published on 25 Mar 2026 - 12:45

score 95 · Answer 11 · 2019-09-02 18:02:32

95

Views

Proving Pascal's Rule : $\binom n k =\binom{n−1}{ k−1}+\binom{n−1} k $

Published on 02 Sep 2019 - 18:02

score 82 · Answer 12 · 2019-09-05 02:47:53

82

Views

Show that$\displaystyle \sum_{t \ge 0} \binom{n}{j+t} \binom{m}{k+t} = \binom {m+n}{n+k-j}$

Published on 05 Sep 2019 - 2:47

score 61 · Answer 13 · 2019-09-08 13:45:44

61

Views

Permutations on circular table so that i cannot go to i or i+1.

Published on 08 Sep 2019 - 13:45

score 98 · Answer 14 · 2019-09-11 15:32:45

98

Views

using sets in combinatorial identity proof

Published on 11 Sep 2019 - 15:32

score 79 · Answer 15 · 2019-09-11 21:49:32

79

Views

Find all $n,k \in \Bbb N^+$ such that $(n-1)!=n^k-1$

Published on 11 Sep 2019 - 21:49

List Question

Does this equation hold in general?

Does this identity with binomial coefficients have a combinatorial interpretation?

Uniformly Distributed Random-Variable With Specific Ordering

Can a upper bound of $\sum_{b=1}^{p-1}\left(\frac{b^2-a^2}{p}\right)\left(\frac{b^2-1}{p}\right)$, $a\in{Z}$, be strictly less than $\sqrt{p}$?

Combinatorial proof of $\sum_{k=0}^{n} \binom{3n-k}{2n} = \binom{3n+1}{n}$

If $a_1 + a_2 + \dots + a_{100}=0$, with $a_1,\dots,a_{100}\in\mathbb{R}$, prove that $a_i+a_j \geq0, i\neq j,$ for at least $99$ $i,j$-pairs

Let, there be a matrix of order $N$ with all distinct entries. Using the given entries, is the sum of determinants of all possible matrices zero?

Bijection between Dyck paths with $k$ peaks and $n+1-k$ peaks

Throwing a die three times - check my proof

Equality like Pascal triangle

Proving Pascal's Rule : $\binom n k =\binom{n−1}{ k−1}+\binom{n−1} k $

Show that$\displaystyle \sum_{t \ge 0} \binom{n}{j+t} \binom{m}{k+t} = \binom {m+n}{n+k-j}$

Permutations on circular table so that i cannot go to i or i+1.

using sets in combinatorial identity proof

Find all $n,k \in \Bbb N^+$ such that $(n-1)!=n^k-1$

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