Four problems about tilings, related to the so-called: Heesch number, isohedral number, $m$-morphic figures, and $\sigma$-morphic figures, can be asked in four variations of the notion of tiling: protosets with more elements, disconnected tiles, colored tiles and tessellations in larger-dimensional spaces. That makes $16$ combinations in total. Five among them have been previously solved in the literature, and one has been partially solved. We here solve seven of the remaining combinations, and additionally complete that partial solution.
@article{10_37236_11813,
author = {Bojan Ba\v{s}i\'c and Aleksa D\v{z}uklevski and Anna Slivkov\'a},
title = {Solutions to seven and a half problems on tilings},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11813},
zbl = {1527.52015},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11813/}
}
TY - JOUR
AU - Bojan Bašić
AU - Aleksa Džuklevski
AU - Anna Slivková
TI - Solutions to seven and a half problems on tilings
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11813/
DO - 10.37236/11813
ID - 10_37236_11813
ER -
%0 Journal Article
%A Bojan Bašić
%A Aleksa Džuklevski
%A Anna Slivková
%T Solutions to seven and a half problems on tilings
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11813/
%R 10.37236/11813
%F 10_37236_11813
Bojan Bašić; Aleksa Džuklevski; Anna Slivková. Solutions to seven and a half problems on tilings. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11813
