7 citations · 42 across the 33 of their papers we have counts for
4 papers · 1 filter
Volume and lattice points counting for the cyclopermutohedron
Ilya Nekrasov, Gaiane Panina
The face lattice of the permutohedron realizes the combinatorics of linearly ordered partitions of the set . Similarly, the cyclopermutohedron is a virtual polytop…
Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle
Gaiane Panina, Alena Zhukova
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…
Point Charges and Polygonal Linkages
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma +1
We investigate the critical points of Coulomb potential of point charges placed at the vertices of a planar polygonal linkage. It is shown that, for a collection of positive charge…
Equilibria of point charges on convex curves
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
We study the equilibrium positions of three points on a convex curve under influence of the Coulomb potential. We identify these positions as orthotripods, three points on the curv…