Generating Functions for Straight Polyomino Tilings of Narrow Rectangles
Mudit Aggarwal and Samrith Ram
Indraprastha Institute of Information Technology Delhi
New Delhi 110020
Let m, k be fixed positive integers.
Determining the generating function for the number of tilings
of an m × n rectangle by
k × 1 rectangles is a
longstanding open problem to which the answer is only
known in certain special cases.
We give an explicit formula for this generating
function in the case where m < 2k.
This result is used to obtain the generating function for the number of
tilings of an m × n × k
box with k × k × 1 bricks.
Full version: pdf,
(Concerned with sequences
Received November 15 2022; revised versions received December 9 2022; December 13 2022; December 20 2022
Published in Journal of Integer Sequences,
January 1 2023.
Journal of Integer Sequences home page