# Richard Stanley: Two Analogues of Pascal's Triangle

Time: Wed 2021-10-06 15.15 - 16.15

Location:

Lecturer: Richard Stanley (M.I.T. and University of Miami)

Abstract: 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.

Zoom meeting ID: 654 5562 3260