### 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 language | English (US) |
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Pages (from-to) | 563-571 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 340 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*,

*340*(4), 563-571. https://doi.org/10.1016/j.disc.2016.12.006

}

*Discrete Mathematics*, vol. 340, no. 4, pp. 563-571. https://doi.org/10.1016/j.disc.2016.12.006

**Colored partitions of a convex polygon by noncrossing diagonals.** / Birmajer, Daniel; Gil, Juan B.; Weiner, Michael D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Colored partitions of a convex polygon by noncrossing diagonals

AU - Birmajer, Daniel

AU - Gil, Juan B.

AU - Weiner, Michael D.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85007530447&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007530447&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2016.12.006

DO - 10.1016/j.disc.2016.12.006

M3 - Article

AN - SCOPUS:85007530447

VL - 340

SP - 563

EP - 571

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 4

ER -