7 citations · 42 across the 33 of their papers we have counts for
42 papers
Affine transverse foliations in sphere bundles
Ilya Alekseev, Ivan Nasonov, Gaiane Panina
Let~ be an oriented sphere bundle supporting a {smooth} affine transverse foliation. We give a new and elementary proof of the following fact:…
Squared Distance Function on the Configuration Space of a planar Spider with Applications to Hooke Energy and Voronoi Distance
Maciej Denkowski, Gaiane Panina, Dirk Siersma
Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intens…
Concurrent normals problem for convex polytopes and Euclidean distance degree
Ivan Nasonov, Gaiane Panina, Dirk Siersma
It is conjectured since long that for any convex body there exists a point in its interior which belongs to at least normals from different points on t…
Cooperative envy-free division
Duško Jojić, Gaiane Panina, Rade Živaljević
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" and divide…
Concurrent normals of immersed manifolds
Gaiane Panina, Dirk Siersma
It is conjectured since long that for any convex body there exists a point in the interior of which belongs to at least normals from different poi…
A note on the concurrent normal conjecture
A. Grebennikov, G. Panina
It is conjectured since long that for any convex body there exists a point in the interior of which belongs to at least normals from different points…
An elementary approach to local combinatorial formulae for the Euler class of a PL spherical fiber bundle
Gaiane Panina
We present an elementary approach to local combinatorial formulae for the Euler class of a fiber-oriented triangulated spherical fiber bundle. The approach is based on sections ave…
Envy-free division in the presence of a dragon
Gaiane Panina, Rade Živaljević
We prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive) player, called the "dragon". There are two basic scenarios. 1. Th…
Envy-free division via configuration spaces
Gaiane Panina, Rade Živaljević
The classical approach to envy-free division and equilibrium problems relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree.…
Equilibrium stressability of multidimensional frameworks
Oleg Karpenkov, Christian Müller, Gaiane Panina +3
We prove an equilibrium stressability criterium for trivalent multidimensional tensegrities. The criterium appears in different languages: (1) in terms of stress monodromies, (2) i…
Optimal colored Tverberg theorems for prime powers
Duško Jojić, Gaiane Panina, Rade T. Živaljević
The type A colored Tverberg theorem of Blagojević, Matschke, and Ziegler provides optimal bounds for the colored Tverberg problem, under the condition that the number of intersecti…
Generalized chessboard complexes and discrete Morse theory
Duško Jojić, Gaiane Panina, Siniša T. Vrećica +1
Chessboard complexes and their generalizations, as objects, and Discrete Morse theory, as a tool, are presented as a unifying theme linking different areas of geometry, topology, a…
Area-perimeter duality in polygon spaces
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail…
Splitting necklaces, with constraints
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove several versions of N. Alon's "necklace-splitting theorem", subject to additional constraints, as illustrated by the following results. (1) The "almost equicardinal neckla…
A universality theorem for stressable graphs in the plane
Gaiane Panina
Universality theorems (in the sense of N. Mnëv) claim that the realization space of a combinatorial object (a point configuration, a hyperplane arrangement, a convex polytope, etc.…
A Tverberg type theorem for collectively unavoidable complexes
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove (Theorem 2.4) that the symmetrized deleted join of a "balanced family" of collectively -unavoidabl…
Compactifications of associated with Alexander self-dual complexes: Chow ring, -classes and intersection numbers
Ilia Nekrasov, Gaiane Panina
An Alexander self-dual complex gives rise to a compactification of , called ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but a…
Extremal areas of polygons with fixed perimeter
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
We consider the configuration space of planar -gons with fixed perimeter, which is diffeomorphic to the complex projective space . The oriented area function…
Geometric presentation for the cohomology ring of polygon spaces
Ilia Nekrasov, Gaiane Panina
We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are…
Diagonal complexes for surfaces of finite type and surfaces with involution
Joseph Gordon, Gaiane Panina
Two related constructions are studied: (1) The diagonal complex and its barycentric subdivision related to a \textit{punctured} oriented surface eq…
Polygons with prescribed edge slopes: configuration space and extremal points of perimeter
Joseph Gordon, Gaiane Panina, Yana Teplitskaya
We describe the configuration space of polygons with prescribed edge slopes, and study the perimeter as a Morse function on . We characterize…
Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons
Ilia Nekrasov, Gaiane Panina, Alena Zhukova
Given a flexible -gon with generic side lengths, the moduli space of its configurations in as well as in is a smooth manifold. It is equipped with…
On the area of constrained polygonal linkages
Gaiane Panina, Dirk Siersma
We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate defini…
Diagonal complexes
Joseph Gordon, Gaiane Panina
Given an -gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace…