Question

Does this equation hold in general?

score 549 · Answer 1 · 2026-04-09 15:18:31

549

Views

Does this equation hold in general?

Published on 09 Apr 2026 - 15:18

score 132 · Answer 2 · 2026-04-09 17:02:19

132

Views

Does this identity with binomial coefficients have a combinatorial interpretation?

Published on 09 Apr 2026 - 17:02

score 171 · Answer 3 · 2026-04-13 05:10:24

171

Views

Uniformly Distributed Random-Variable With Specific Ordering

Published on 13 Apr 2026 - 5:10

score 43 · Answer 4 · 2026-04-16 19:46:45

43

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 16 Apr 2026 - 19:46

score 582 · Answer 5 · 2026-04-15 00:44:20

582

Views

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

Published on 15 Apr 2026 - 0:44

score 86 · Answer 6 · 2026-04-16 15:47:38

86

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 16 Apr 2026 - 15:47

score 76 · Answer 7 · 2026-04-17 07:29:19

76

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 17 Apr 2026 - 7:29

score 942 · Answer 8 · 2026-05-11 02:20:15

942

Views

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

Published on 11 May 2026 - 2:20

score 55 · Answer 9 · 2026-04-16 01:20:15

55

Views

Throwing a die three times - check my proof

Published on 16 Apr 2026 - 1:20

score 496 · Answer 10 · 2026-05-10 17:55:17

496

Views

Equality like Pascal triangle

Published on 10 May 2026 - 17:55

score 98 · Answer 11 · 2026-04-16 09:15:15

98

Views

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

Published on 16 Apr 2026 - 9:15

score 85 · Answer 12 · 2026-04-17 01:31:16

85

Views

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

Published on 17 Apr 2026 - 1:31

score 64 · Answer 13 · 2026-04-15 11:19:54

64

Views

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

Published on 15 Apr 2026 - 11:19

score 100 · Answer 14 · 2026-04-15 04:56:41

100

Views

using sets in combinatorial identity proof

Published on 15 Apr 2026 - 4:56

score 82 · Answer 15 · 2026-04-14 19:15:26

82

Views

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

Published on 14 Apr 2026 - 19:15

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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