Combinatorics of Two-Toned Tilings

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Phyllis Chinn, Humboldt State University
Jacob N. Scott '11, Harvey Mudd CollegeFollow
Greg Simay, Burbank Power and Water

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

11-2011

Abstract

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.

Comments

Archived with permission from The Fibonacci Association.

Rights Information

© 2011 Fibonacci Association

Recommended Citation

Benjamin, Arthur T., Phyllis Chinn, Jacob N. Scott and Greg Simay. "Combinatorics of Two Toned Tilings." The Fibonacci Quarterly, Vol. 49, No. 4, pp. 290-297, November 2011.