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- #1

- Jan 17, 2013

- 1,667

Can we define ''Non-crossing'' partitions in words . I have seen the visualization of these partitions and the number of them is calculated using the Catalan's numbers.

- Thread starter ZaidAlyafey
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- Thread starter
- #1

- Jan 17, 2013

- 1,667

Can we define ''Non-crossing'' partitions in words . I have seen the visualization of these partitions and the number of them is calculated using the Catalan's numbers.

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- #2

- Jan 26, 2012

- 4,193

There's a nice picture illustrating noncrossing partitions.is a partition in which no two blocks "cross" each other, i.e., if a and b belong to one block and x and y to another, they are not arranged in the order a x b y. If one draws an arch based at a and b, and another arch based at x and y, then the two arches cross each other if the order is a x b y but not if it is a x y b or a b x y. In the latter two orders the partition { { a, b }, { x, y } } is noncrossing.

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- #3

- Jan 17, 2013

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Yes, I already saw this . But I am surprised to know that this is the only explanation! I mean it should have a mathematical definition '' can be described by words '' .In the wiki, it says that a noncrossing partition There's a nice picture illustrating noncrossing partitions.

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- #4

- Jan 26, 2012

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- Thread starter
- #5

- Jan 17, 2013

- 1,667

I actually meant something else .But now I got the general idea , thanks .