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DTSTART;TZID=America/Los_Angeles:20190402T121500
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CREATED:20190206T180617Z
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UID:1196-1554207300-1554210600@colleges.claremont.edu
SUMMARY:Fibonacci and Lucas analogues of binomial coefficients and what they count (Curtis Bennett\, CSULB)
DESCRIPTION: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 \n$${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ \nsince 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.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-curtis-bennett-csulb/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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