Cutting 4 by n grids into two congruent pieces

Cutting 4 by n grids into two congruent pieces
By Robert Dougherty-Bliss, Natalya Ter-Saakov, and Doron Zeilberger
.pdf .tex

Pour Jean-Paul Delahaye, avec admiration

Posted: Oct. 15, 2025

In the March 2025 issue of the French monthly "Pour La Science", Jean-Paul Delahaye proved (in collaboration with his épouse, Martine Raison) that there are 2ⁿ⁺¹-n-1 ways to cut a 3 by 2n discrete rectangle into two congruent connected pieces. We do the analogous problem for a 4 by n rectangle.

appendix (with another, more detailed, theorem that also follows from the grammar, see procedure GFa(x,a) in the Maple package.

Maple package

Decoupage.txt, A Maple package to study cutting of a 4 by n rectangle into two connected congruent pieces

C program

Decoupage.c

Sample Input and Output for Decoupage.txt

If you want to see all 4 by n Graham matrices for n between 2 and 12
the input file produces output file
If you want to see the generating function for the number of ways of 4 by n (what we call in the paper) Graham matrices, in other words number of ways of cutting a 4 by n (colorless) checkerboard into two congruent pieces
the input file produces output file

Articles of Doron Zeilberger
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