Forced symmetric rigidity in non-Euclidean periodic and crystallographic frameworks

Establish combinatorial characterizations of forced symmetric rigidity for infinite periodic and crystallographic frameworks in non-Euclidean normed planes, under both fixed and flexible lattice representations, and for finite frameworks with symmetries or normed-plane structures beyond the cases already characterized.

Background

The paper states that existing combinatorial characterizations in non-Euclidean normed spaces are limited to finite frameworks with reflection or half-turn symmetry in the ℓ1 and ℓ∞ norms. It identifies the corresponding problems for other finite symmetries, other normed planes, and infinite periodic or crystallographic frameworks with forced symmetry as unresolved, for both fixed and flexible lattice representations.