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Vladimir I. Danilov

Principal Researcher, Doctor of Sciences in Mathematics
E-mail: vdanilov43 (at) mail.ru

Selected Publications

(Links lead to full texts of papers in pdf format)

Mathematics

Tropical Plucker functions and their bases (with Koshevoy G., Karzanov A.) In: "Contemporary Mathematics", 495 (2009), 127-158. [336 kB]

B2-cristals: axioms, structures, models (with Koshevoy G. and Karzanov A.) Journal of Combinatorial Theory, 2009, Series A, 116, 265-289. [267 kB]

Choice functions and extensive operators (with G. Koshevoy) Order, 2009, 26, 69-94. [225 kB]

The crossing model for regular An-crystals (with Karzanov A., Koshevoy G.) Journal of Algebra, 2008, 320, 9, 3398-3424. [506 kB]

The Robinson-Shensted-Knuth correspondence and bijections of commutativity and associativity (with G.A. Koshevoy) Izvestia RAN, math. series, 2008, v. 72, 4, 67-96 (in Russian, English version in Izvestiya: Mathematics). [448 kB]

Existence of fixed points for mappings of finite sets (with G.Koshevoy), Matematicheskie zametki, 2007, 82, 201-206 (in Russian). [164 kB]

The octahedron recurrence and RSK-correspondence (with G.Koshevoy) Seminar Lotharinngien de Combinatoire 2007, B54An. [239 kB]

Combinatorics of regular A2-crystals (with A.Karzanov, G.Koshevoy). Journal of Algebra, 2007, 310, 218-234. [206 kB]

Discrete strip-concave functions, Gelfand-Tsetlin patterns, and related polyhedra. (with A.V.Karzanov, G.A.Koshevoy) em Journal of Combinatorial Theory, A 2005, v.112, 175-193. [249 kB]

Arrays and Young tableaux, Uspehi Matematicheskih Nauk, 60, n. 2 (2005) 79-142 (in Russian). [568 kB]

Discrete convexity and unimodularity - I (with G.Koshevoy), Advances in Mathematics 189 (2004) 301-324. [333 kB]

Gross substitution, Discrete convexity, and Submodularity (with Koshevoy G. and Lang C.) Discrete and Applied Mathematics 2003, 131(2), 238-258. [186 kB]

Nilpotent operators and discrete concave functions (with G.Koshevoy), Izvestia of RAS (ser. math.), 2003, 67, n. 1 (in Russian). [263 kB]

Discrete convexity and Hermitian matrices (with G.Koshevoy), Proc. Steklov Inst. Math., vol. 241, Moscow: Nauka Publ., 2003, pp. 68-89 (in Russian). [334 kB]

Integer convexity, Proc. of I.R.Shafarevich seminar, Second issue, Moscow, 2000, 48-66 (in Russian). [251 kB]

Maximal unimodular systems of vectors (with V. Grishukhin), European Journal of Combinatorics, 1999, 20, 507-526.

De Rham complex on toroidal variety, in Algebraic Geometry (Chicago, IL, 1989), Springer-Verlag, Berlin, 1991, 26-38.

Decomposition of some birational morphisms, Izvestia of the USSR Academy of Sciences, math. ser., 1980, 44 (in Russian).

Newton polyhedra and vanishing cohomologies, Functional Analysis and Applications, 1979, 13 (in Russian).

The geometry of toric varieties, Uspehi Matematicheskih Nauk, 1978, 32(2) (in Russian).

Polyhedra of schemas and algebraic varieties, Matematicheskij Sbornik, 1975, 97 (in Russian).

Automorphisms of affine surfaces: I,II (with M. H. Gizatullin), Izvestia of the USSR Academy of Sciences, math. ser., 1975, 39, 1977, 41 (in Russian).

Rings with discrete divisor class group, Matematicheskij Sbornik, 1970, 83 (in Russian).

On the Samuel conjecture, Matematicheskij Sbornik, 1968, 77 (in Russian).

Mathematical Economics

Modeling of non-commuting dimensions, Journal of the New Economic Association, 2009, ¹ 1-2, 10-36. (in Russian) [305 kB]

Economies with the innovation goods (with G.Koshevoy), Economika i Matematicheskie Metody, 2009, 45, n. 1. (in Russian) [251 kB]

Decision-making under non-classical uncertainty (with Lambert-Mogiliansky A.) in Quantum Interaction. Proceedings of the Second Quantum Interaction Symposium (QI-2008) (eds. Peter D. Bruza and other), London, 2008, 83-86. [115 kB]

Measurable systems and behavioral sciences (with Lambert-Mogiliansky A.) Mathematical Social Sciences, 2008, 55, 315-340. [492 kB]

A phantom of Coase theorem, Economics of Contemporary Russia, 2008, 2(41), 39-45 (in Russian). [191 kB]

A new characterization of the path independent choice functions (with G.Koshevoy) Math. Soc. Sciences, 2006, 51, 238-245.

Mathematics of Plott choice functions. (with G.Koshevoy) Math. Social Sciences, 2005, 49, 245-272. [297 kB]

Random choice and random preferences, Economika i Matematicheskie Metody, 2005, 41 n. 1, 94-105 (in Russian) [479 kB]

Piece-wise linear gross-substitutable utility functions (with C.Lang), Economika i matematicheskie metody, 2001, 37, no. 4 (in Russian) [307 kB]

Substitutes, complements and equilibria in two-sided market models. (with Koshevoy G.A. Lang C.) in Advances in Economic Design (eds. M.R. Sertel and S.Koray), Springer, Berlin, 2001, 105-123. [291 kB]

Discrete convexity and equilibria in economies with indivisible goods and money. (with G.Koshevoy, K.Murota) Math. Soc. Sciences, 2001, 41 (3), 251-273. [145 kB]

Equilibrium in an economy of information goods (with A.I. Sotskov, G.A. Koshevoy), in Markets, Information and Uncertainty (ed. G.Chichilnisky), Cambridge University Press, 1999, 26-44.

On Scarf ’s theorem, Economika i Matematicheskie Metody, 1999, 35, 137-139 (in Russian). [128 kB]

A model of economic equilibrium in the market for information goods, (with G. A. Koshevoy and A. I. Sotskov), in Contemporary Economic Issues, v. 4 (M. Sertel, Ed.), N. Y., 1999, 161-182.

Rational choice under convex conditions (with A. I. Sotskov), in Constructing Scalar-valued Objective Functions (A. Tangian and J. Gruber, Eds.) Springer-Verlag, Berlin, 1997, 53-63.

Equilibrium analysis of an economy with innovations (with G. A. Koshevoy and A. I. Sotskov), Journal of Mathematical Economics, 1997, 27, 195-226.

Equilibrium in a market of intellectual goods (with G. A. Koshevoy and A. I. Sotskov), Mathematical Social Sciences, 1994, 27, 133-144.

Economic equilibrium in a market of intellectual goods (with G. A. Koshevoy and A. I. Sotskov) Economika i Matematicheskie Metody, 1993, 29, 607-616 (in Russian).

On strongly consistent social choice functions (with A. I. Sotskov), Journal of Mathematical Economics, 1993, 22, 327-346.

Equilibria in an economy with overlapping generations, Economika i Matematicheskie Metody, 1993, 29, 26-38 (in Russian).

Implementation via Nash equilibria, Econometrica, 1991, v.59.

Implementation of social choice correspondences via coalitional equilibria (with A. I. Sotskov), Economika i Matematicheskie Metody, 1991, 27, 720-732 (in Russian).

A generalized economic equilibrium (with A. I. Sotskov), Journal of Mathematical Economics, 1990, 19, 341-356.

Coalitionally stable mechanisms of social choice (with A. I. Sotskov), Economika i Matematicheskie Metody, 1988, 24 (in Russian).

Stable blockings in social choice mechanisms (with A. I. Sotskov), Economika i Matematicheskie Metody, 1987, 23 (in Russian).

Balanced states and theorems about the core (with A. I. Sotskov), Optimization, 1987, 41 (in Russian).

Aggregation of dichotomic preferences, Mathematical Social Sciences, 1985, 13.

Structure of binary rules of preference aggregation, Economika i Matematicheskie Metody, 1984, 20 (in Russian).

Models of social choice, Tekhnicheskaja Kibernetika, 1983 (in Russian).

Algebraic aspects of social choice, in Researches in Mathematical Economics and Control Theory, CEMI, Moscow, 1982 (in Russian).

Articles in Press

Equilibria with indivisible goods and package-utilities (with G. Koshevoy and C. Lang), Math. Oper. Res. [609 kB]

Expected Utility Theory under Non-Classical Uncertainty. Theory and Decision (with Lambert-Mogiliansky A.) [236 kB]

Knowledge spaces from a topological point of view, Journal of Mathematical Psychology

Books

Lectures on Game Theory, NES, Moscow, 2002. (in Russian) [0,98 MB]

Social Choice Mechanisms (with A. I. Sotskov), Springer-Verlag, Berlin, 2002 (191 pages). [1,17 MB]

Lectures on fixed points, NES, Moscow, 1998. (in Russian) [359 kB]

Algebraic Geometry II (with V. A. Iskovskikh and I. R. Shafarevich), Springer-Verlag, Berlin, 1996.

Algebraic Geometry I (with V. V. Shokurov), Springer-Verlag, Berlin, 1994.

Social choice mechanisms (with A. I. Sotskov), Nauka, Moscow, 1991. (in Russian)

© CEMI RAS 2009