Graduation Year
2016
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Arthur Benjamin
Reader 2
Nicholas Pippenger
Terms of Use & License Information
Rights Information
© 2016 Robert L Bennett
Abstract
The Fibonomial coefficients are a generalization of the binomial coefficients with a rather nice combinatorial interpretation. While the ordinary binomial coefficients count lattice paths in a grid, the Fibonomial coefficients count the number of ways to draw a lattice path in a grid and then Fibonacci-tile the regions above and below the path in a particular way. We may forgo a literal tiling interpretation and, instead of the Fibonacci numbers, use an arbitrary function to count the number of ways to "tile" the regions of the grid delineated by the lattice path. When the function is a combinatorial sequence such as the Lucas numbers or the q-numbers, the total number of "tilings" is some multiple of a generalized binomial coefficient corresponding to the sequence chosen.
Recommended Citation
Bennett, Robert, "Fibonomial Tilings and Other Up-Down Tilings" (2016). HMC Senior Theses. 84.
https://scholarship.claremont.edu/hmc_theses/84
Source Fulltext
/home/students/hmc_2016/rbennett/rbennett-2016-thesis/rbennett-2016-thesis.pdf
