7 citations · 11 across the 5 of their papers we have counts for
6 papers · 1 filter
Mediatic graphs
J. -Cl. Falmagne, S. Ovchinnikov
Any medium can be represented as an isometric subgraph of the hypercube, with each token of the medium represented by a particular equivalence class of arcs of the subgraph. Such a…
Partial cubes: structures, characterizations, and constructions
Sergei Ovchinnikov
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djoković's and Winkler's relations play an important role in the theor…
Cubical token systems
Sergei Ovchinnikov
The paper deals with combinatorial and stochastic structures of cubical token systems. A cubical token system is an instance of a token system, which in turn is an instance of a tr…
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…
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.