Dissecting a square into congruent polygons
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1
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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.
@article{DMTCS_2020_22_1_a21,
author = {Rao, Hui and Ren, Lei and Wang, Yang},
title = {Dissecting a square into congruent polygons},
journal = {Discrete mathematics & theoretical computer science},
year = {2020-2021},
volume = {22},
number = {1},
doi = {10.23638/DMTCS-22-1-21},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-21/}
}
TY - JOUR AU - Rao, Hui AU - Ren, Lei AU - Wang, Yang TI - Dissecting a square into congruent polygons JO - Discrete mathematics & theoretical computer science PY - 2020-2021 VL - 22 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-21/ DO - 10.23638/DMTCS-22-1-21 LA - en ID - DMTCS_2020_22_1_a21 ER -
%0 Journal Article %A Rao, Hui %A Ren, Lei %A Wang, Yang %T Dissecting a square into congruent polygons %J Discrete mathematics & theoretical computer science %D 2020-2021 %V 22 %N 1 %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-21/ %R 10.23638/DMTCS-22-1-21 %G en %F DMTCS_2020_22_1_a21
Rao, Hui; Ren, Lei; Wang, Yang. Dissecting a square into congruent polygons. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1. doi: 10.23638/DMTCS-22-1-21
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