Colored partitions of a convex polygon by noncrossing diagonals

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Convex polygon
Partition
Polynomials
Polygon
Bell Polynomials
Congruent
Recurrence relation
Modulo
Restriction
Partial
Polynomial
Integer

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

@article{c87be083382d4791b289c6535cfca4e5,
title = "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.",
author = "Daniel Birmajer and Gil, {Juan B.} and Weiner, {Michael D.}",
year = "2017",
month = "4",
day = "1",
doi = "10.1016/j.disc.2016.12.006",
language = "English (US)",
volume = "340",
pages = "563--571",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "4",

}

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

In: Discrete Mathematics, Vol. 340, No. 4, 01.04.2017, p. 563-571.

Research output: Contribution to journalArticle

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 -