1. bookVolume 3 (2016): Issue 6 (December 2016)
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
access type Open Access

Construction and Enumeration of Circuits Capable of Guiding a Miniature Vehicle

Published Online: 08 Dec 2016
Volume & Issue: Volume 3 (2016) - Issue 6 (December 2016)
Page range: 5 - 42
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
Abstract

In contrast to traditional toy tracks, a patented system allows the creation of a large number of tracks with a minimal number of pieces, and whose loops always close properly. These circuits strongly resemble traditional self-avoiding polygons (whose explicit enumeration has not yet been resolved for an arbitrary number of squares) yet there are numerous differences, notably the fact that the geometric constraints are different than those of self-avoiding polygons. We present the methodology allowing the construction and enumeration of all of the possible tracks containing a given number of pieces. For small numbers of pieces, the exact enumeration will be treated. For greater numbers of pieces, only an estimation will be offered. In the latter case, a randomly construction of circuits is also given. We will give some routes for generalizations for similar problems.

Keywords

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