Discrete CATS Seminar
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U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2011 - 2012

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"Combinatorial interpretations of binomial coefficient
analogues related to Lucas sequences"

Stuart Hamilton

University of Kentucky

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Monday, April 2, 2012

2:00 pm

Location: 845 Patterson Office Tower

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Abstract:
This paper concerns polynomials {n} in s and t defined by {0}=0, {1}=1
and {n}=s{n-1}+t{n-2}. The binomial coefficient analogues of the title
are defined by {nk}={n}!{k}!{n-k}! where {n}!={1}{2}...{n}. For
particular choices of s and t and suitable initial conditions, {n} is
a generating function for the number of tilings of a strip of n-1
consecutive squares by monominoes and dominoes, or such a strip with
its ends joined. These ideas are extended to two dimensions to show
that partitions represented by Ferrers diagrams can be interpreted
using the binomial coefficient analogue.