Colored partitions of a convex polygon by noncrossing diagonals

@article{Birmajer2017ColoredPO,
  title={Colored partitions of a convex polygon by noncrossing diagonals},
  author={Daniel Birmajer and J. Gil and M. Weiner},
  journal={Discret. Math.},
  year={2017},
  volume={340},
  pages={563-571}
}
For any positive integers a and b , we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to b modulo a . For the number of such partitions made by a fixed number of diagonals, we give both a recurrence relation and an explicit representation in terms of partial Bell polynomials. We use basic properties of these polynomials to efficiently incorporate restrictions on the type of polygons allowed in the partitions. 
A family of Bell transformations
Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs
Some relatives of the Catalan sequence

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