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Corpus ID: 13232684

Combinatorics of Two-Toned Tilings

@inproceedings{Benjamin2011CombinatoricsOT,
title={Combinatorics of Two-Toned Tilings},
author={Arthur T. Benjamin and Phyllis Z. Chinn and Jacob N. Scott and Greg Simay},
year={2011}
}

We introduce the function a(r, n) which counts tilings of length n+ r that utilize white tiles (whose lengths can vary between 1 and n) and r identical red squares. These tilings are called two-toned tilings. We provide combinatorial proofs of several identities satisfied by a(r, n) and its generalizations, including one that produces kth order Fibonacci numbers. Applications to integer partitions are also provided.

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Harvey Mudd College, Claremont, CA 91711 E-mail address: benjamin@hmc.edu Department of Mathematics CA 95521 E-mail address: phyllis.chinn@humboldt.edu Harvey Mudd College

MSC2010: 05A19 Department of Mathematics CA 91711 E-mail address: jnscott@hmc.edu Burbank Water and Power