Combinatorics and Graph Theory

•  Richard Stanley, MIT
•  Two Analogues of Pascal's Triangle
•  02/03/2021
•  3:00 PM - 3:50 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Bruce E Sagan (bsagan@msu.edu)

Pascal's triangle is closely associated with the expansion of the product $(1+x)^n$. We will discuss two analogous arrays of numbers that are associated with the products $\prod_{i=0}^{n-1} \left(1+x^{2^i}+x^{2^{i+1}}\right)$ and $\prod_{i=1}^n \left(1+x^{F_{i+1}}\right)$, where $F_{i+1}$ is a Fibonacci number. All three arrays are special cases of a two-parameter family that might be interesting to investigate further.

Contact

Department of Mathematics
Michigan State University