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Counting Train Track Layouts

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Train track layouts with switches not only provide children with hours of amusement, they provide us with a number of interesting mathematical problems. How many different layouts can be made from a set of track with two switches? What do we mean by different? We develop two different but reasonable definitions for equivalence of train track layouts, and in each case, count the number of equivalence classes. We use such tools as two-term recurrences, directed graphs, and eigenvalues of incidence matrices to learn about the fascinating mathematics of train track layouts.

Document Type: Research Article

Publication date: December 1, 2006

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