In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.
@article{10_37236_2212,
author = {Anthony Nixon and Elissa Ross},
title = {Periodic rigidity on a variable torus using inductive constructions},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/2212},
zbl = {1305.05057},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2212/}
}
TY - JOUR
AU - Anthony Nixon
AU - Elissa Ross
TI - Periodic rigidity on a variable torus using inductive constructions
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2212/
DO - 10.37236/2212
ID - 10_37236_2212
ER -
%0 Journal Article
%A Anthony Nixon
%A Elissa Ross
%T Periodic rigidity on a variable torus using inductive constructions
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2212/
%R 10.37236/2212
%F 10_37236_2212
Anthony Nixon; Elissa Ross. Periodic rigidity on a variable torus using inductive constructions. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/2212
