Question

Binomial identity for bijection $\mathbb N\times\mathbb N\to\mathbb N$

score 96 · Answer 1 · 2026-03-30 14:20:08

96

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Binomial identity for bijection $\mathbb N\times\mathbb N\to\mathbb N$

Published on 30 Mar 2026 - 14:20

score 551 · Answer 2 · 2016-07-19 14:22:22

551

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How to find$\sum_{i,j,k\in \mathbb{Z}}\binom{n}{i+j}\binom{n}{j+k}\binom{n}{i+k}$ for $n \in \mathbb{N}$

Published on 19 Jul 2016 - 14:22

score 126 · Answer 3 · 2016-07-20 01:04:35

126

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Closed formula for ${r \choose 1}+{r \choose 2}\cdots{r \choose w}$ where $w < r$

Published on 20 Jul 2016 - 1:04

score 355 · Answer 4 · 2026-03-30 16:23:25

355

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Finite summation including binomial coefficients and double factorials

Published on 30 Mar 2026 - 16:23

score 202 · Answer 5 · 2026-03-31 20:25:44

202

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Sum $\sum\limits_{j=k}^n\binom{j}{k}(-1)^j$

Published on 31 Mar 2026 - 20:25

score 394 · Answer 6 · 2026-04-10 16:42:43

394

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Combinatorics problem involving binomial coefficient

Published on 10 Apr 2026 - 16:42

score 249 · Answer 7 · 2026-04-10 16:16:28

249

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A sum involving binomial coefficients and its evaluation using the Gamma function

Published on 10 Apr 2026 - 16:16

score 72 · Answer 8 · 2026-03-30 16:23:50

72

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Find a map on a power set with certain combinatorial properties

Published on 30 Mar 2026 - 16:23

score 50 · Answer 9 · 2026-03-30 16:22:54

50

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Find an explicit map with certain combinatorial properties

Published on 30 Mar 2026 - 16:22

score 1.5k · Answer 10 · 2016-07-22 22:09:48

1.5k

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Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $

Published on 22 Jul 2016 - 22:09

score 180 · Answer 11 · 2016-07-23 11:58:02

180

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Combinatorial identity's algebraic proof without induction.

Published on 23 Jul 2016 - 11:58

score 48 · Answer 12 · 2026-03-30 18:05:29

48

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Prove that: ${^{n}\mathrm{C}_{k}} = {^{n-1}\mathrm{C}_{k-1}}+{^{n-1}\mathrm{C}_{k}}$

Published on 30 Mar 2026 - 18:05

score 310 · Answer 13 · 2026-03-30 23:55:43

310

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Problem related to series of binomial coefficients

Published on 30 Mar 2026 - 23:55

score 1k · Answer 14 · 2016-07-24 11:24:46

1k

Views

Notation for binomial coefficient set

Published on 24 Jul 2016 - 11:24

score 1k · Answer 15 · 2026-04-09 05:49:32

1k

Views

How do I find the terms of an expansion using combinatorial reasoning?

Published on 09 Apr 2026 - 5:49

List Question

Binomial identity for bijection $\mathbb N\times\mathbb N\to\mathbb N$

How to find$\sum_{i,j,k\in \mathbb{Z}}\binom{n}{i+j}\binom{n}{j+k}\binom{n}{i+k}$ for $n \in \mathbb{N}$

Closed formula for ${r \choose 1}+{r \choose 2}\cdots{r \choose w}$ where $w < r$

Finite summation including binomial coefficients and double factorials

Sum $\sum\limits_{j=k}^n\binom{j}{k}(-1)^j$

Combinatorics problem involving binomial coefficient

A sum involving binomial coefficients and its evaluation using the Gamma function

Find a map on a power set with certain combinatorial properties

Find an explicit map with certain combinatorial properties

Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $

Combinatorial identity's algebraic proof without induction.

Prove that: ${^{n}\mathrm{C}_{k}} = {^{n-1}\mathrm{C}_{k-1}}+{^{n-1}\mathrm{C}_{k}}$

Problem related to series of binomial coefficients

Notation for binomial coefficient set

How do I find the terms of an expansion using combinatorial reasoning?

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