eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2020-06-29
vol. 22 no. 1
Combinatorics
10.23638/DMTCS-22-1-21
6022
journal article
Dissecting a square into congruent polygons
Hui Rao
Lei Ren
Yang Wang
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.
https://dmtcs.episciences.org/6022/pdf
Mathematics - Combinatorics
52B45, 05C45