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Results tagged with catalan-numbers
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user 81488
The Catalan numbers form the sequence of numbers starting 1,1,2,5,14,42,... with explicit formula $\frac{1}{n+1}\binom{2n}{n}$. It counts many combinatorial objects like planar binary trees, triangulations, noncrossing partitions, Dyck paths, etc. See https://oeis.org/A000108
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Distribution of the area statistic for Catalan paths
Notice that the number of Catalan paths of area at least $cn^{\frac{3}{2}+\varepsilon}$ is less than the number of all paths that deviate from the horizontal axis by at least $n^{\frac{1}{2}+\varepsil …
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