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Catalan number

math Maturity 7-9

Some numbers follow a pattern.

Dyck lattice D4.svg
Dyck lattice D4.svg
They help us count many things. We can use them to count ways to draw mountains. They also count ways to make shapes. These numbers help us see how things fit. Can you find a pattern?

44 words
🖼️ Images & Media (13)
File:Noncrossing partitions 5.svg
Noncrossing partitions 5.svg
File:Dyck lattice D4.svg
Dyck lattice D4.svg
File:Catalan 4 leaves binary tree example.svg
Catalan 4 leaves binary tree example.svg
File:Tamari lattice, trees.svg
Tamari lattice, trees.svg
File:Catalan number 4x4 grid example.svg
Catalan number 4x4 grid example.svg
File:Tamari lattice, hexagons.svg
Tamari lattice, hexagons.svg
File:Catalan-Hexagons-example.svg
Catalan-Hexagons-example.svg
File:Catalan stairsteps 4.svg
Catalan stairsteps 4.svg
File:Catalan number-path reflection.svg
Catalan number-path reflection.svg
File:Catalan number exceedance example.png
Catalan number exceedance example.png
File:Catalan number swapping example.png
Catalan number swapping example.png
File:Catalan number algorithm table.png
Catalan number algorithm table.png

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📚 Content adapted from Wikipedia | Readability: FK 11.3 | Vital Level 5