Holger Langenau: Squaring the square -- New methods for determining the number of perfect square packings

Author(s):

Holger Langenau

Title:

Holger Langenau: Squaring the square -- New methods for determining the number of perfect square packings

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 07, 2017

Mathematics Subject Classification:

    52C15 []
    05B40 []
    90C35 []

Abstract:

Given a square with integer side length n, we ask for the number of different ways to divide it into sub-squares, considering only the list of parts. We enumerate all possible lists and check whether a placement with those squares is possible. In order to do this, we propose a new algorithm for creating perfect square packings.

Keywords:

Square, Packing, Partition, Backtracking

Language:

English

Publication time:

01/2018