7 citations · 11 across the 2 of their papers we have counts for
5 papers
Weak order complexes
Sergei Ovchinnikov
The paper presents geometric models for the set WO of weak orders on a finite set. In particulary, WO is modeled as a set of vertices of a cubical subdivision of a permutahedron. T…
The lattice dimension of a tree
Sergei Ovchinnikov
The lattice dimension of a graph G is the minimal dimension of a cubic lattice in which G can be isometrically embedded. We prove that the lattice dimension of a tree with n leaves…
Boolean representation of manifolds and functions
Sergei Ovchinnikov
It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the poi…
Max-Min Representation of Piecewise Linear Functions
Sergei Ovchinnikov
It is shown that a piecewise linear function can be represented as a Max-Min polynomial of its linear components.
Universal metric spaces according to W. Holsztynski
S. Ovchinnikov
We show, following W. Holsztynski, that there exists a continuous metric d on the set of real numbers R such that any finite metric space is isometrically embeddable into (R,d).