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

Stuart Hamilton
University of Kentucky

Monday, April 2, 2012
2:00 pm
Location: 845 Patterson Office Tower

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.