14 citations · 73 across the 14 of their papers we have counts for
14 papers
Flexing infinite frameworks with applications to braced Penrose tilings
Sean Dewar, Jan Legerský
A planar framework -- a graph together with a map of its vertices to the plane -- is flexible if it allows a continuous deformation preserving the distances between adjacent vertic…
Zero-sum cycles in flexible non-triangular polyhedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular…
Zero-sum cycles in flexible polyhedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously deformed preserving the shape of its faces, then the…
Bracing frameworks consisting of parallelograms
Georg Grasegger, Jan Legerský
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinato…
Combinatorics of Bricard's octahedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We re-prove the classification of flexible octahedra, obtained by Bricard at the beginning of the XX century, by means of combinatorial objects satisfying some elementary rules. Th…
FlexRiLoG -- A SageMath Package for Motions of Graphs
Georg Grasegger, Jan Legerský
In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using s…
On the Classification of Motions of Paradoxically Movable Graphs
Georg Grasegger, Jan Legerský, Josef Schicho
Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown rec…
Flexible placements of graphs with rotational symmetry
Sean Dewar, Georg Grasegger, Jan Legerský
We study the existence of an -fold rotationally symmetric placement of a symmetric graph in the plane allowing a continuous deformation that preserves the symmetry and the dista…
On the existence of paradoxical motions of generically rigid graphs on the sphere
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge…
On the maximal number of real embeddings of minimally rigid graphs in , and
Evangelos Bartzos, Ioannis Z. Emiris, Jan Legerský +1
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space or on a sphere and which in addition satisfy certain edge length…
Graphs with Flexible Labelings allowing Injective Realizations
Georg Grasegger, Jan Legerský, Josef Schicho
We consider realizations of a graph in the plane such that the distances between adjacent vertices satisfy the constraints given by an edge labeling. If there are infinitely many s…
On the maximal number of real embeddings of spatial minimally rigid graphs
Evangelos Bartzos, Ioannis Emiris, Jan Legerský +1
The number of embeddings of minimally rigid graphs in is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though…
Construction of Algorithms for Parallel Addition
Jan Legerský, Milena Svobodová
An algebraic number with no conjugate of modulus 1 can serve as the base of a numeration system with parallel addition, i.e., the sum of two op…
Graphs with Flexible Labelings
Georg Grasegger, Jan Legerský, Josef Schicho
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinator…