In how Many Ways can you Rectangle a Rectangle?
By Pablo Blanco, Robert Dougherty-Bliss, Natalya Ter-Saakov, and Doron Zeilberger
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.tex
[YET TO BE WRITTEN]
Posted: April 2026
We use experimental mathematics, both rigorous and semi-rigorous, to derive generating functions for computing the number of ways to tile
a rectangle by rectangular tiles. We also consider the easier problem of tiling by square tiles.
Maple package
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RectTile.txt,
A Maple package to compute generating functions for enumerating tilings of a rectangle by rectangular tiles. Also by square tiles.
Sample Input and Output for RectTile.txt
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If you want to see the generating functions for enumerating of an m by n rectangle into rectangular tiles, for m from 1 to 6, using the GRAMMAR
the input file produces
output file
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If you want to see the generating functions for enumerating of an m by n rectangle into rectangular tiles, for m from 1 to 9, using the Joshua Smith and Helena Verrill approach
the input file produces
output file
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If you want to see the generating functions for enumerating of an m by n rectangle into rectangular tiles, for m from 1 to 5, using GUESSING
the input file produces
output file
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If you want to see the generating functions for enumerating of an m by n rectangle into SQUARE tiles, for m from 1 to 9, using GUESSING
the input file produces
output file
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If you want to see the generating functions for weight-enumerating of an m by n rectangle into RECTANGULAR tiles, according to the weight wNumberOfEdges for m from 1 to 6
(done fully rigorously)
the input file produces
output file
Articles of Doron Zeilberger
Pablo Blanco's Home Page
Robert Dougherty-Bliss's Home Page
Natalya Ter-Saakov's Home Page
Doron Zeilberger's Home Page