Loading Events

« All Events

  • This event has passed.

Fibonacci and Lucas analogues of binomial coefficients and what they count (Curtis Bennett, CSULB)

April 2 @ 12:15 pm - 1:10 pm

A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number.  For example, the Fibonomial

$${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$

since the first six Fibonacci numbers are 1, 1, 2, 2, 5, and 8.  Curiously the Fibonomials are always integers, raising the combinatorial question:  what do they count?  In this talk we introduce and provide a little history of the Fibonomials.  We then provide a simple object the Fibonomials enumerate.  We will use this new object to prove various Fibonomial analogues of standard identities on binomial coefficients and discuss further generalizations including the Lucanomials.

Details

Date:
April 2
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Curtis Bennett (CSULB)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map

Details

Date:
April 2
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Curtis Bennett (CSULB)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map