Hadamard Products and Tilings

Details Hadamard Products and Tilings Hadamard Products and Tilings

2009-03-03

arxiv.org/abs/0903.0594v2

Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.4

Mathematics

Combinatorics

11 pages

Scientific paper

Louis W. Shapiro gave a combinatorial proof of a bilinear generating function for Chebyshev polynomials equivalent to the formula 1/(1-ax-x^2) * 1/(1-bx-x^2) = (1-x^2)/(1-abx-(2+a^2+b^2)x^2 -abx^3+x^4), where * denotes the Hadamard product. In a similar way, by considering tilings of a 2 by n rectangle with 1 by 1 and 1 by 2 bricks in the top row, and 1 by 1 and 1 by n bricks in the bottom row, we find an explicit formula for the Hadamard product 1/(1-ax-x^2) * x^m/(1-bx-x^n).

Affiliated with

Also associated with

No associations

Rating

Hadamard Products and Tilings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hadamard Products and Tilings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hadamard Products and Tilings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653797