October 29, 2019
Dr. Jordan Tirrell, Professor of Mathematics, Washington College, will present "Counting with Fibonacci numbers: Fibotorials, Fibonomials, and other Fibothings". Free pizza. Everyone welcome!.
Formulas involving division come up quite often in counting problems. You may have seen some before, like the formula for binomial coefficients, which can be written as a quotient of factorials. For fun, let's replace the ordinary numbers 1, 2, 3, 4, 5, 6, 7,... in this formula with Fibonacci numbers 1, 1, 2, 3, 5, 8, 12,... . So we'll replace a factorial with a Fibotorial (for example, the sixth Fibotorial is 1*1*2*3*5*8=240), and our binomial coefficients become Fibonomial coefficients. Shockingly, these are always integers! Integers often count things. Binomial coefficients count things, and Fibonacci numbers count things, but what do Fibonomial coefficients count? I first heard about this question in a talk when I was an undergraduate. Spoiler alert: it has now been answered. But don't worry, I have plenty of unanswered questions about Fibothings to share.
Further information
- Location: Tome 115
- Time: 12:00 pm - 1:00 pm
- Cost: Free