Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay
Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay
All HMC Faculty Publications and Research
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.