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A question about series involving Catalan numbers in some sort

score 89 · Answer 1 · 2017-11-02 23:06:10

89

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A question about series involving Catalan numbers in some sort

Published on 02 Nov 2017 - 23:06

score 2.6k · Answer 2 · 2017-11-20 19:40:49

2.6k

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finding the formula for nth catalan number as total number of combinations of balanced n pair parenthesis.

Published on 20 Nov 2017 - 19:40

score 219 · Answer 3 · 2026-03-28 21:26:49

219

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Combinatorial justification for $C_{11}-C_{10}=\binom{12+9}9-2\binom{12+9-1}{9-1}$

Published on 28 Mar 2026 - 21:26

score 1.9k · Answer 4 · 2017-11-27 18:57:53

1.9k

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Show $\frac 1 3 C_0+\left(\frac 2 3 \right)\left(\frac 1 3 \right)^2 C_1+\left(\frac 2 3\right)^2 \left(\frac 1 3 \right)^3 C_2 +\dots =\frac 1 2$

Published on 27 Nov 2017 - 18:57

score 261 · Answer 5 · 2017-12-05 07:59:07

261

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Creating a bijection between Dyck paths and 231-avoiding permutations

Published on 05 Dec 2017 - 7:59

score 42 · Answer 6 · 2017-12-09 09:03:10

42

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Number of sequences $a_1, \dots,a_{12}$ with conditions

Published on 09 Dec 2017 - 9:03

score 1.5k · Answer 7 · 2011-01-05 00:09:43

What is a convenient way to convert a string of balanced parentheses to a corresponding "multiplication ordering" or rooted binary tree?

score 2.5k · Answer 8 · 2011-02-07 07:55:23

2.5k

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Explanation/Intuition behind why $C_n$ counts the number of triangulations of a convex $n+2$-gon?

Published on 07 Feb 2011 - 7:55

score 852 · Answer 9 · 2011-04-29 05:42:23

852

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Show that the Catalan numbers are given by this recurrence relation

Published on 29 Apr 2011 - 5:42

score 4.6k · Answer 10 · 2011-04-30 12:28:42

4.6k

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How do the Catalan numbers turn up here?

Published on 30 Apr 2011 - 12:28

score 459 · Answer 11 · 2026-03-28 14:55:32

459

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Path-type description for (faces of) associahedra?

Published on 28 Mar 2026 - 14:55

score 1.4k · Answer 12 · 2026-03-29 03:53:19

1.4k

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Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths

Published on 29 Mar 2026 - 3:53

score 394 · Answer 13 · 2011-11-18 07:11:38

394

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On the path diagram of a partition

Published on 18 Nov 2011 - 7:11

score 1.2k · Answer 14 · 2012-01-02 14:40:10

1.2k

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Using the Catalan numbers

Published on 02 Jan 2012 - 14:40

score 408 · Answer 15 · 2012-02-10 09:53:02

408

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Generating function of shifted Catalan Numbers

Published on 10 Feb 2012 - 9:53

List Question

A question about series involving Catalan numbers in some sort

finding the formula for nth catalan number as total number of combinations of balanced n pair parenthesis.

Combinatorial justification for $C_{11}-C_{10}=\binom{12+9}9-2\binom{12+9-1}{9-1}$

Show $\frac 1 3 C_0+\left(\frac 2 3 \right)\left(\frac 1 3 \right)^2 C_1+\left(\frac 2 3\right)^2 \left(\frac 1 3 \right)^3 C_2 +\dots =\frac 1 2$

Creating a bijection between Dyck paths and 231-avoiding permutations

Number of sequences $a_1, \dots,a_{12}$ with conditions

What is a convenient way to convert a string of balanced parentheses to a corresponding "multiplication ordering" or rooted binary tree?

Explanation/Intuition behind why $C_n$ counts the number of triangulations of a convex $n+2$-gon?

Show that the Catalan numbers are given by this recurrence relation

How do the Catalan numbers turn up here?

Path-type description for (faces of) associahedra?

Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths

On the path diagram of a partition

Using the Catalan numbers

Generating function of shifted Catalan Numbers

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