We define a geometric transformation of Euclidean Travelling Salesman Problem (TSP)
tours that leads to a new formulation of the TSP. For every Euclidean TSP n-city tour, it is …

The isolation and nondegeneracy of constrained extrema arising in geometric problems and
mathematical models of electrostatics are studied. In particular, it is proved that a convex …

We describe the configuration space SS of polygons with prescribed edge slopes, and study
the perimeter PP as a Morse function on S S. We characterize critical points of PP (these are …

We consider the oriented area function A on the moduli space M (P) of mechanical linkage P
representing a planar multiple pendulum. For generic lengths of the sides of P, it is proved …

For a polygonal linkage, we produce a fast navigation algorithm on its configuration space.
The basic idea is to approximate M (L) by the vertex-edge graph of the cell decomposition of …

The article discusses a study on the cyclic configurations of spherical polygons that satisfies
the Euler constraint. It states that the method used in the analysis is based on the …

We introduce a perfect discrete Morse function on the moduli space of a polygonal linkage.
The ingredients of the construction are:(1) the cell structure on the moduli space, and (2) the …

We study polygon spaces arising from planar configurations of necklaces with some of the
beads fixed and some of the beads sliding freely. These spaces include configuration …

Построена точная дискретная функция Морса на пространстве модулей плоского
шарнирного многоугольника. Использована клеточная структура на пространстве …

Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle -
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