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University of Mississippi

(Visible) Tilings of Squares and Hypercubes

Abstract

dc:description.abstract

More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction techniques are introduced, especially methods of generating tilings from tilings with fewer tiles. For some small values of n, I determine all tilings of the unit square with n tiles. I have found a best possible upper bound for a visible tiling, that is a tiling which every tile shares a face with the unit square. Furthermore, I generalize this result to higher dimensions for visible tilings.

Degree

thesis:*
Name thesis:degree_name
M.S. in Mathematics
Level thesis:degree_level
Thesis
Discipline thesis:degree_discipline
Mathematics
Year dc:date.available
2014

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Burt, John Randall
Contributors dc:contributor
  • William Staton
  • Talmadge James Reid
  • Bing Wei

Subjects

dc:subject × 1

Identifiers

dc:identifier.*
Repository record dc:identifier
https://egrove.olemiss.edu/etd/1326
OAI identifier oai:identifier
oai:egrove.olemiss.edu:etd-2325

Chain of custody

source
Harvested from
University of Mississippi
Base URL
egrove.olemiss.edu/do/oai/
Last updated
2026-07-24
Source record
OAI-PMH GetRecord
citation

Burt, John Randall. (Visible) Tilings of Squares and Hypercubes. Thesis thesis, 2014. https://egrove.olemiss.edu/etd/1326