Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 1.11.2022 |
| Speaker: | Jan Legerský, FIT, České vysoké učení technické v Praze |
| Title: | Flexing infinite frameworks with applications to braced Penrose tilings |
| Abstract: | 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 vertices. Extending a recent previous result, we prove that a connected graph with a countable vertex set can be realized as a flexible framework if and only if it has a so-called NAC-coloring. The tools developed to prove this result are then applied to frameworks where every 4-cycle is a parallelogram, and countably infinite graphs with -fold rotational symmetry. With this, we determine a simple combinatorial characterization that determines whether the 1-skeleton of a Penrose rhombus tiling with a given set of braced rhombi will have a flexible motion, and also whether the motion will preserve 5-fold rotational symmetry. |
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