Minimal Dispersion of Large Volume Boxes in the Cube

• Author / Creator

  Kurt S. MacKay

• In this note we present a construction which improves the best
  known bound on the minimal dispersion of large volume boxes in the unit cube. The dispersion of a subset of the cube is the supremal volume over all axis parallel boxes in the cube which do not intersect the given subset. The minimal n-point dispersion is the infimal dispersion over all subsets of the cube containing n points. Define the large volume regime as the set of real volumes greater than 14 . In this note we work exclusively in the large volume setting. The construction presented in this paper yields a dimension independent upper bound which is an improvement on, and is proportional to the square root of the best known bound in this regime. We also show that some intermediate estimates are sharp, given that the dimension is taken to be
  larger than a specified volume-dependent constant.

• Subjects / Keywords

  • Discrete Geometry
  • Dispersion
  • Geometric Analysis
  • Convex Analysis
  • Volume
  • Cube
  • Rectangle
  • Packing

• Graduation date

  Fall 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-fege-v984

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.