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## 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:

Lenny Fukshansky
Gizem Karaali

## Other

Speaker Name
Curtis Bennett (CSULB)

## Venue

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

## Details

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

Lenny Fukshansky
Gizem Karaali

## Other

Speaker Name
Curtis Bennett (CSULB)

## Venue

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