Colored partitions of a convex polygon by noncrossing diagonals
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 DOI:
 10.48550/arXiv.1503.05242
 arXiv:
 arXiv:1503.05242
 Bibcode:
 2015arXiv150305242B
 Keywords:

 Mathematics  Combinatorics;
 05A17;
 05A19
 EPrint:
 11 pages, 3 figures, Submitted for publication