# Gleb A. Koshevoy

Principal Researcher, Doctor of Sciences in Mathematics**E-mail:**koshevoy (at) cemi.rssi.ru

## Publications in Refereed Journals

Tropical Plucker functions and their bases, In: "Contemporary Mathematics", 495 (2009), 127-158 (with V. Danilov and A. Karzanov)

Choice
functions and extensive operators, *ORDER*, 26(2009), 69-94 (with V.Danilov)

B2
crystals: axioms, structure, models, *J. Combin. Theory*, Series A, 116(2009),
265-289 (with V. Danilov and A. Karzanov) E-print: arXiv:
math/0708.2198

The crossing model for regular An-crystals, *J.
of Algebra*, 320 (2008), 3398-3424 (with V. Danilov and A. Karzanov) E-print:
arXiv: math.CO/0612360

The
Robinson-Schensted-Knuth correspondence and the bijections of commutativity and
associativity, *Math. Izvestiya Russ. Acad. Sciences*, 72:4(2008), 689-716
(in Russian) (English transl. in *Russian Acad. Sci. Izv. Math.*) (with V.
Danilov) E-print: arXiv: math.CO/0504299

Matroids
on convex geometries (cg-matroids), *Discrete Mathematics*, 307(2007), 1936-1950
(with S. Fujishige and Y. Sano)

Combinatorics of A2-crystals, *J. of Algebra*,
310(2007), 218-234 (with V. Danilov and A. Karzanov)

Existence of Fixed
Points for Mappings of Finite Sets, *Mat. Zametki*, 82:2(2007), 201-206 (in
Russian; with V.I. Danilov) (English translation in *Mathematical Notes*)

The
octahedron recurrence and RSK-correspondence, *Seminar Lotharinngien de Combinatoire*,
B54An(2006) (with V. Danilov)

Equilibria for pooling situations, *International
J. Game Theory*, 34:1(2006), 123-130 (with S. Tjis and S. Miquel)

Competitive
equilibria in economies with multiple indivisible and multiple divisible commodities
, *Journal of Mathematical Economics* 42(2006), 216-226 (with D. Talman)

A
new characterization of path-independence,* Mathematical Social Sciences*,
51(2006), 238-245 (with V.I. Danilov)

Arrays and the combinatorics of Young
tableaux, *Uspekhi Matem. Nauk* , 60:2(2005), 79-142, (in Russian; with V.I.
Danilov) (English transl. in *Russian Mathematical Surveys*)

Mathematics
of Plott choice functions, *Mathematical Social Sciences*, 49(2005), 245-272
(with V. Danilov and A. Karzanov)

Discrete strip-concave functions, Gelfand-Tsetlin
patterns, and related polyhedra, *J. Comb. Theory*, Ser. A 112(2005), 175-193
(with V. Danilov and A. Karzanov), E-print: arXiv:
math.CO/0404298

Choice functions and closure operators with the anti-exchange
property, *Discrete and Applied Mathematics*, 147(2005), 81-89

Discrete
Convexity and Unimodularity. I. *Advances in Mathematics*, 189(2004), 301-324
(with V. Danilov)

A general existence theorem of zero points, *J. of Optimization
Theory and Application*, 120:2(2004), 375-394 (with J.J. Hering, D. Talman
and Z. Yang)

On the geometry of multivariate L1 objective functions,*
Allg. Statist. Archive*, 88(2004), 137-154 (with J. Mottonen and H. Oja)

Discrete
convexity and Nilpotent operators, *Math. Izvestiya Russ. Acad. Sciences*,
67(2003), 3-20 (in Russian; with V. Danilov)

Gross substitution, Discrete
convexity, and Submodularity, *Discrete and Applied Mathematics*, 131:2(2003),
283-298 (with V. Danilov and Ch. Lang)

A scatter matrix estimate based on
zonotope, *The Annals of Statistics*, 31:5(2003), 1439-1459 (with J. Mottonen
and H. Oja)

Plott choice functions and convex geometries, *Economika i
Matematicheskie Metody*, 39:3(2003), 88-95 (in Russian)

The Tukey depth
characterizes the atomic measure, *Journal of Multivariate Analysis*, 83(2002),
360-364

Equilibria in Economies with Indivisible Goods and Money, *Mathematical
Social Sciences*, 41(2001), 251-273 (with V. Danilov and K. Murota)

Cores
of cooperative games, superdifferentials of functions and Minkowski difference
of sets, *Journal of Mathematical Analysis and Appl.*, 247(2000), 1-14 (with
V.I. Danilov)

Choice functions and abstract convex geometries, *Mathematical
Social Sciences*, 38(1999), 35-44

Measuring multidimensional concentration:
A geometrical approach, *Allg. Statist. Archive*, 83(1999), 172-188 (with
K. Mosler)

Lift zonoids, random convex hulls and the variability of random
vectors, *Bernoulli*, 4(1998), 377-399 (with K. Mosler)

The Lorenz
zonotope and multivariate majorizations, *Social Choice and Welfare*, 15(1998),
1-14

Distributive lattices and products of capacities, *Journal of Mathematical
Analysis and Appl.*, 219(1998), 427-441

Zonoid trimming for multivariate
distributions, *The Annals of Statistics*, 25(1997), 1998-2017 (with K. Mosler)

Equilibrium
analysis of economies with innovations, *Journal of Mathematical Economics*,
27(1997), 195-228 (with V.I. Danilov and A.I. Sotskov)

Homotopy properties
of Pareto aggregation rules, *Social Choice and Welfare*, 14(1997) 295-302

Multivariate Gini indices, *Journal of Multivariate Analysis*, 60(1997),
252-277 (with K. Mosler)

The Lorenz zonoid of a multivariate distribution,
*Journal of the American Statistical Association*, 91(1996): 873–882 (with
K. Mosler)

Multivariate Lorenz majorization, *Social Choice and Welfare*,
12(1995), 93-102

Topological approach to social choice with infinite population,
*Mathematical Social Sciences*, 27(1994) 145-157 (with B.A. Efimov)

Equilibrium on a Market of Intellectual Goods, *Mathematical Social Sciences*,
27(1994) 133-144 (with V.I. Danilov and A.I. Sotskov)

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

Multivariate
inequality indices and orderings on a product of symmetric groups, *Economika
i Matematicheskie Metody*, 29(1993), 245-256 (in Russian)

On the Existence
of a Technical Efficiency Criterion, *Journal of Economic Theory*, 55(1991),
121-144 (with A.V. Dmitruk)

Curves of infinite genus that are uniformizable
in the sense of Schottky, *Russian Mathematical Surveys* , 44(1989), 207-208

Теоремы
существования равновесия для моделей экономики с двумя видами цен, *Оптимизация*,
43(1988), 130-141