Sergei Ovchinnikov
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Recent Publications

"Graphs and Cubes", 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.

  1. Media theory - representations and examples, Discrete Applied Mathematics, 156 (2008), 1197-1219.
  2. Representations of T-similarity relations, Fuzzy Sets and Systems, 159 (2008), 2211-2220.
  3. Cubical token systems, Mathematical Social Sciences, 56 (2008) 149-165.
  4. Partial cubes: structures and constructions, Discrete Mathematics, 308 (2008) 5597-5621.
  5. 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.
  6. 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.
  7. Discrete picewise linear functions, European Journal of Combinatorics, 91 (2010) 1283-1294.
  8. Series with inverse function terms, The College Mathematics Journal 42(4) (2011) 283-288.

Complete list of publications