When searching for small 4-configurations of points and lines, polycyclic configurations, in which every symmetry class of points and lines contains the same number of elements, have proved to be quite useful. In this paper we construct and prove the existence of a previously unknown $(21_4)$ configuration, which provides a counterexample to a conjecture of Branko Grünbaum. In addition, we study some of its most important properties; in particular, we make a comparison with the well-known Grünbaum-Rigby configuration. We show that there are exactly two $(21_{4})$ geometric polycyclic configurations and seventeen $(21_{4})$ combinatorial polycyclic configurations. We also discuss some possible generalizations.
@article{10_37236_12405,
author = {Leah Wrenn Berman and G\'abor G\'evay and Toma\v{z} Pisanski},
title = {On a new \((21_4)\) polycyclic configuration},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12405},
zbl = {1556.51004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12405/}
}
TY - JOUR
AU - Leah Wrenn Berman
AU - Gábor Gévay
AU - Tomaž Pisanski
TI - On a new \((21_4)\) polycyclic configuration
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12405/
DO - 10.37236/12405
ID - 10_37236_12405
ER -
%0 Journal Article
%A Leah Wrenn Berman
%A Gábor Gévay
%A Tomaž Pisanski
%T On a new \((21_4)\) polycyclic configuration
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12405/
%R 10.37236/12405
%F 10_37236_12405
Leah Wrenn Berman; Gábor Gévay; Tomaž Pisanski. On a new \((21_4)\) polycyclic configuration. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12405
