Question

Combinatorial interpretation of an identity for expressing Stirling number of the second kind using binomial coefficients

score 98 · Answer 1 · 2026-03-30 03:38:04

98

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Combinatorial interpretation of an identity for expressing Stirling number of the second kind using binomial coefficients

Published on 30 Mar 2026 - 3:38

score 189 · Answer 2 · 2026-03-29 02:36:14

189

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Hales-Jewett Number $HJ(2,r)$

Published on 29 Mar 2026 - 2:36

score 27 · Answer 3 · 2021-11-17 23:52:52

27

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Extended Pascal's Triangle Identity -General identity.

Published on 17 Nov 2021 - 23:52

score 256 · Answer 4 · 2026-03-29 07:39:26

256

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More elegant proofs of $\binom a2+\binom b2\leq \binom{a+b-1}2$

Published on 29 Mar 2026 - 7:39

score 75 · Answer 5 · 2021-11-23 00:52:23

75

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Combinatorial justification on $n^{2} = (n-1)^{2} + 2(n-1) +1$

Published on 23 Nov 2021 - 0:52

score 3.2k · Answer 6 · 2021-11-23 06:16:06

3.2k

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Intriguing moves with the $3\times3\times3$ Rubiks cube

Published on 23 Nov 2021 - 6:16

score 163 · Answer 7 · 2026-03-29 23:24:06

163

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Non-crossing partitions without singletons

Published on 29 Mar 2026 - 23:24

score 102 · Answer 8 · 2021-11-29 20:12:30

102

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$\sum_{i=k}^{z} \frac{(-1)^{i-k} {z\choose i}{i\choose k}}{i+1} = \frac{1}{z+1} $ - combinatorial identity

Published on 29 Nov 2021 - 20:12

score 92 · Answer 9 · 2021-12-04 03:03:23

92

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proving $\binom{n-1}{k} - \binom{n-1}{k-2} = \binom{n}{k} - \binom{n}{k-1} $

Published on 04 Dec 2021 - 3:03

score 134 · Answer 10 · 2021-12-05 23:09:26

134

Views

Combi Problem - Proving Existence of a row

Published on 05 Dec 2021 - 23:09

score 347 · Answer 11 · 2026-03-29 17:25:27

347

Views

A recurrence for the number of non-crossing partitions without singletons, using Dyck paths

Published on 29 Mar 2026 - 17:25

score 152 · Answer 12 · 2021-12-08 20:16:49

152

Views

Combinatorial identity from squaring the binomial expansion

Published on 08 Dec 2021 - 20:16

score 26 · Answer 13 · 2021-12-13 10:43:55

26

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Prove using the method of double counting: $3^n =\sum_{k=0}^n \dbinom{n}{k} \sum_{j=0}^k \dbinom{k}{j}$

Published on 13 Dec 2021 - 10:43

score 155 · Answer 14 · 2026-02-23 12:34:37

155

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Given $c$ and $a_i$, how many solutions does $c=\sum\nolimits_{i}{{{n}_{i}}{{a}_{i}}}$ have?

Published on 23 Feb 2026 - 12:34

score 175 · Answer 15 · 2026-03-29 23:26:57

175

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Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$

Published on 29 Mar 2026 - 23:26

List Question

Combinatorial interpretation of an identity for expressing Stirling number of the second kind using binomial coefficients

Hales-Jewett Number $HJ(2,r)$

Extended Pascal's Triangle Identity -General identity.

More elegant proofs of $\binom a2+\binom b2\leq \binom{a+b-1}2$

Combinatorial justification on $n^{2} = (n-1)^{2} + 2(n-1) +1$

Intriguing moves with the $3\times3\times3$ Rubiks cube

Non-crossing partitions without singletons

$\sum_{i=k}^{z} \frac{(-1)^{i-k} {z\choose i}{i\choose k}}{i+1} = \frac{1}{z+1} $ - combinatorial identity

proving $\binom{n-1}{k} - \binom{n-1}{k-2} = \binom{n}{k} - \binom{n}{k-1} $

Combi Problem - Proving Existence of a row

A recurrence for the number of non-crossing partitions without singletons, using Dyck paths

Combinatorial identity from squaring the binomial expansion

Prove using the method of double counting: $3^n =\sum_{k=0}^n \dbinom{n}{k} \sum_{j=0}^k \dbinom{k}{j}$

Given $c$ and $a_i$, how many solutions does $c=\sum\nolimits_{i}{{{n}_{i}}{{a}_{i}}}$ have?

Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$

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