6 research outputs found
Dyck paths with coloured ascents
We introduce a notion of Dyck paths with coloured ascents. For several ways
of colouring, we establish bijections between sets of such paths and other
combinatorial structures, such as non-crossing trees, dissections of a convex
polygon, etc. In some cases enumeration gives new expression for sequences
enumerating these structures.Comment: 14 pages, 11 figure
Triangulating stable laminations
We study the asymptotic behavior of random simply generated noncrossing
planar trees in the space of compact subsets of the unit disk, equipped with
the Hausdorff distance. Their distributional limits are obtained by
triangulating at random the faces of stable laminations, which are random
compact subsets of the unit disk made of non-intersecting chords coded by
stable L\'evy processes. We also study other ways to "fill-in" the faces of
stable laminations, which leads us to introduce the iteration of laminations
and of trees.Comment: 34 pages, 5 figure