• 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}
}```
• Published 2011
• Mathematics
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.
2 Citations

## Tables from this paper

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## References

SHOWING 1-7 OF 7 REFERENCES
Proofs that Really Count: The Art of Combinatorial Proof
• Mathematics
• 2003
1. Fibonacci identities 2. Lucas identities 3. Gibonacci identities 4. Linear recurrences 5. Continued fractions 6. Binomial identities 7. Alternating sign binomial identities 8. Harmonic numbers and
Discrete and Combinatorial Mathematics: An Applied Introduction
PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS. 1. Fundamental Principles of Counting. The Rules of Sum and Product. Permutations. Combinations: The Binomial Theorem. Combinations with Repetition. The
A new family of functions and their relationship to compositions and k-Fibonacci numbers
• Congressus Numerantium
• 2009
Simay, A New family of functions and their relationship to compositions and k-Fibonacci numbers
• Congressus Numerantium,
• 2009
A New family of functions and their relationship to compositions and kFibonacci numbers
• Congressus Numerantium
• 2009
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
• 1968