Colored partitions of a convex polygon by noncrossing diagonals

Daniel Birmajer, Juan B. Gil, Michael D. Weiner

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)563-571
Number of pages9
JournalDiscrete Mathematics
Volume340
Issue number4
DOIs
StatePublished - Apr 1 2017

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