Rao, Hui and Ren, Lei and Wang, Yang - Dissecting a square into congruent polygons

dmtcs:6022 - Discrete Mathematics & Theoretical Computer Science, June 29, 2020, vol. 22 no. 1 - https://doi.org/10.23638/DMTCS-22-1-21
Dissecting a square into congruent polygons

Authors: Rao, Hui and Ren, Lei and Wang, Yang

We study the dissection of a square into congruent convex polygons. Yuan \emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime number $\geq 3$, it is true that the tile must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the tile is a convex $q$-gon with $q\geq 6$ or it is a right-angle trapezoid.


Volume: vol. 22 no. 1
Section: Combinatorics
Published on: June 29, 2020
Submitted on: January 13, 2020
Keywords: Mathematics - Combinatorics,52B45, 05C45


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