,
by Sergei Ovchinnikov,
Springer, 2011.
Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph
and partial cube theories. Many exercises, along with historical notes, are included at the end of every chapter, and
readers are encouraged to explore the exercises fully, and use them as a basis for research projects.
"Media Theory",
by D.Eppstein, J.-Cl.Falmagne and S.Ovchinnikov,
Springer, 2008. Sample chapter.
The focus of this book is a mathematical structure modeling a physical or biological system that can be in any
of a number of 'states'. Each state is characterized by a set of binary features, and differs from some other
neighbor state or states by just one of those feature. The evolution of such a system over time is considered. Such a structure is
analyzed from algebraic and probabilistic (stochastic) standpoints.
- Media theory - representations and examples,
Discrete Applied Mathematics, 156 (2008), 1197-1219.
- Representations of T-similarity relations,
Fuzzy Sets and Systems, 159 (2008), 2211-2220.
- Cubical token systems, Mathematical Social Sciences,
56 (2008) 149-165.
- Partial cubes: structures and constructions, Discrete Mathematics,
308 (2008) 5597-5621.
- Geometric representations of weak orders, in:
Uncertainty and Intelligent Information Systems, B. Bouchon-Meunier, R.R. Yager, C. Marsala, and M.
Rifqi eds, World Scientific Publishing Co Pte Ltd (Singapore) (2008), 447-456.
- Mediatic Graphs, (with J.-Cl. Falmagne), in:
The Mathematics of Preference, Choice and Order, S.J Brams, W.V. Gehrlein, F. Roberts eds,
Springer (2009), 325-343.
- Discrete picewise linear functions, European Journal of Combinatorics,
91 (2010) 1283-1294.
- Series with inverse function terms, The College Mathematics Journal
42(4) (2011) 283-288.
Complete list of
publications