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Section: New Results

Formal description of catalan numbers

Participant : José Grimm.

Catalan number can be defined by a recurrence, or by explicit formulas using binomial numbers. An important property is Cn+1=knCkCn-k. The easiest way to prove this formula is to use Dyck paths.

A Dyck path of size 2n is a sequence l of integers +1 and -1 so that the sum sk of the k first terms is 0 for k2n and s2n=0. The relation between Dyck paths and Catalan numbers is easy to prove and then properties of Dyck paths are quite simple to state and verify.

The proofs have been done with the Math-Components library.