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Results tagged with catalan-numbers
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user 52896
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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Domination relationship between generalized Dyck Paths
In short, we are seeking an injection between generalized Dyck paths that end at a certain height into the set of paths of the same length that end at a lower height such that the image path stays bel …
- 457
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Dyck paths weighted by height profile
We are interested in a question concerning a weight function on Dyck paths that penalizes visits to higher heights.
Let $\rho$ be a parameter. Let $D_k$ be the set of all nearest neighbor random walk …
- 457