73 citations · 86 across the 11 of their papers we have counts for
11 papers
Discrete piecewise linear functions
Sergei Ovchinnikov
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions th…
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…
Fundamentals of media theory
Sergei Ovchinnikov
Media theory is a new branch of discrete applied mathematics originally developed in mid-nineties to deal with stochastic evolution of preference relations in political science and…
Media theory: representations and examples
Sergei Ovchinnikov
In this paper we develop a representational approach to media theory. We construct representations of media by well graded families of sets and partial cubes and establish the uniq…