<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Construction and Enumeration of Circuits Capable of Guiding a Miniature Vehicle

Centre de Recherche et d’Innovation sur le Sport, Université Claude Bernard,

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Construction and Enumeration of Circuits Capable of Guiding a Miniature Vehicle"}

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...

Construction and Enumeration of Circuits Capable of Guiding a Miniature Vehicle

Publié en ligne: 08 déc. 2016

Pages: 5 - 42

DOI: https://doi.org/10.1515/rmm-2016-0006

Mots clés
closed paths, toy tracks, combinatorics, exact and asymptotic enumeration

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Construction and Enumeration of Circuits Capable of Guiding a Miniature Vehicle

Publié en ligne: 08 déc. 2016

Pages: 5 - 42

DOI: https://doi.org/10.1515/rmm-2016-0006

Mots clésclosed paths, toy tracks, combinatorics, exact and asymptotic enumeration

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
closed paths, toy tracks, combinatorics, exact and asymptotic enumeration