We consider minimum-perimeter lattice animals, providing a set of conditions which are sufficient for a lattice to have the property that inflating all minimum-perimeter animals of a certain size yields (without repetitions) all minimum-perimeter animals of a new, larger size. We demonstrate this result on the two-dimensional square and hexagonal lattices. In addition, we characterize the sizes of minimum-perimeter animals on these lattices that are not created by inflating members of another set of minimum-perimeter animals.
@article{10_37236_10770,
author = {Gill Barequet and Gil Ben-Shachar},
title = {Minimum-perimeter lattice animals and the constant-isomer conjecture},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10770},
zbl = {1496.05024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10770/}
}
TY - JOUR
AU - Gill Barequet
AU - Gil Ben-Shachar
TI - Minimum-perimeter lattice animals and the constant-isomer conjecture
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10770/
DO - 10.37236/10770
ID - 10_37236_10770
ER -
%0 Journal Article
%A Gill Barequet
%A Gil Ben-Shachar
%T Minimum-perimeter lattice animals and the constant-isomer conjecture
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10770/
%R 10.37236/10770
%F 10_37236_10770
Gill Barequet; Gil Ben-Shachar. Minimum-perimeter lattice animals and the constant-isomer conjecture. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10770
