Department of Mathematics

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 (

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.



Department of Mathematics
Michigan State University
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College of Natural Science