Semigroups of polygons whose vertices define a~centered partition of~$\mathbb R^n$
Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 55-73
Voir la notice de l'article provenant de la source Math-Net.Ru
A partition $\mathfrak F$ of a Euclidean space into finite subsets has subgroup property $\mathsf{SP}$ if the family of the convex hulls of the leaves of $\mathfrak F$ constitutes a subgroup with respect to the Minkowski addition. If $\mathfrak F$ consists of orbits of a finite linear groups then $\mathsf{SP}$ is equivalent to the fact that the group is a Coxeter group. In this article, this assertion is proved only under the assumption of continuity and centrality of $\mathfrak F$ (this means that every leaf is inscribed in some sphere centered at zero). An example is given of a noncentered partition satisfying $\mathsf{SP}$ (such partitions cannot be Coxeter partitions).
@article{MT_2012_15_1_a2,
author = {V. M. Gichev and I. A. Zubareva and E. A. Mescheryakov},
title = {Semigroups of polygons whose vertices define a~centered partition of~$\mathbb R^n$},
journal = {Matemati\v{c}eskie trudy},
pages = {55--73},
publisher = {mathdoc},
volume = {15},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2012_15_1_a2/}
}
TY - JOUR AU - V. M. Gichev AU - I. A. Zubareva AU - E. A. Mescheryakov TI - Semigroups of polygons whose vertices define a~centered partition of~$\mathbb R^n$ JO - Matematičeskie trudy PY - 2012 SP - 55 EP - 73 VL - 15 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MT_2012_15_1_a2/ LA - ru ID - MT_2012_15_1_a2 ER -
%0 Journal Article %A V. M. Gichev %A I. A. Zubareva %A E. A. Mescheryakov %T Semigroups of polygons whose vertices define a~centered partition of~$\mathbb R^n$ %J Matematičeskie trudy %D 2012 %P 55-73 %V 15 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MT_2012_15_1_a2/ %G ru %F MT_2012_15_1_a2
V. M. Gichev; I. A. Zubareva; E. A. Mescheryakov. Semigroups of polygons whose vertices define a~centered partition of~$\mathbb R^n$. Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 55-73. http://geodesic.mathdoc.fr/item/MT_2012_15_1_a2/