Everything About ___
Live briefing

Everything about Rectangulations

Discrete mathematics decomposition

In discrete mathematics, a rectangulation is a decomposition of a rectangle into finitely many interior-disjoint rectangles. The size of a rectangulation describes the number of rectangles used in the decomposition. A segment of a rectangulation is a maximal straight line segment, which is not contained in a side of. The neighbors of a segment are those segments with an endpoint on If no four rectangles meet in a point the rectangulation is called generic . Furthermore, every generic rectangulation of size has exactly segments. This article will consider every rectangulation to be generic, if not stated otherwise. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: RectangulationsA 5-minute orientation
  2. Skim a recent paper: An Upper Bound for the Number of Rectangulations of a Planar Point SetInfluential work since 2022
  3. Pick up a classic book: Report on Sind rectangulation, 1926-30The most-reprinted book on the subject
  4. Read the landmark paper: The Hopf algebra of diagonal rectangulationsCited 26 times
  5. Go sideways: Guillotine partitionA closely related topic
  6. Go sideways: Constraint graph (layout)A closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. Definitions
  2. Bijections to permutation classes
  3. Estimates on the number of rectangulations on planar point sets
  4. Binary search trees and rectangulations
  5. Quadrangulation
  6. Rectangulations in higher dimensions

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics