1. A.I. Barvinok, Homology type of spaces of configurations of structurally stable type in C^2 (Russian), Matematicheskie Zametki , 39 (1986), N 1, 108-112, translated in Mathematical Notes of the Academy of Sciences of the USSR , 60-62, MR 88b:58036.

2. A.I. Barvinok, Symmetric systems of linear inequalities and G -invariant polyhedra (Russian), Optimizatsiya , 40(57) (1987), 111-120, MR 89f:05008.

3. A.I. Barvinok, On topological properties of spaces of polytopes, in: Topology and Geometry - Rohlin Seminar , 495-500, Lecture Notes in Math , 1346 (1988), Springer, Berlin-New York, MR 90c:52012.

4. A.I. Barvinok, Singularities of fields of convex polyhedra and the Pareto optimum problem (Russian), in: Global analysis and nonlinear equations (Russian) Novoe Global. Anal. , Voronezh Gos. Univ., Voronezh, 1988, 108-117, MR 90k:58047.

5. A.I. Barvinok and A.M. Vershik, Convex hulls of orbits of representations of finite groups, and combinatorial optimization (Russian), Funktsional. Anal. i Prilozhen. , 22 (1988), N 3, 66-67, translated in Funct. Anal. Appl. , 224-225, MR 90a:20024.

6. A.I. Barvinok, A.M. Vershik, Methods of representation theory in combinatorial optimization problems (Russian), Izv. Akad. Nauk SSSR, ser. Tekhn. Kibernet. , 1988, N 6, 64-71, translated in Soviet J. Comput. Systems Sci. , 27 (1989), N 5, 1-7, MR 91e:90086.

7. A.I. Barvinok, Combinatorial Theory of Polytopes with Symmetry and its Applications to Combinatorial Optimization Problems (Russian), Doctorate Thesis, Leningrad State University, Leningrad, 1988.

8. A.I. Barvinok, The method of Newton sums in problems of combinatorial optimization (Russian), Diskretnaya Matematika , 2 (1990), N 1, 3-15, translated in Discrete Mathematics and its Applications , 1 (1991), N 4, 349-363, MR 91e:90087.

9. A.I. Barvinok, Computational complexity of immanents and representations of the full linear group (Russian) Funktsional. Anal. i Prilozhen. , 24 (1990), N 2, 74-75, translated in Funct. Anal. Appl. 144-145, MR 92c:15008.

10. A.I. Barvinok, The method of statistical sums in combinatorial optimization problems (Russian), Algebra i analiz , 2 (1990), N 5, 63-79, translated in Leningrad Math. J. , 987-1002, MR 92b:90171.

11. A.I. Barvinok, A.M. Vershik, Polynomial-time computable approximation of families of semi-algebraic sets and combinatorial complexity (Russian), in: Trudy Leningradskogo Matematicheskogo Obshestva , vol. 1, Leningrad State University, 1990, 8-26, translated in Amer. Math. Soc. Transl. (2) , 155 (1993), 1-17, MR 92f:14065.

12. A.I. Barvinok, Combinatorial optimization problems, statistical sums, and representations of the general linear group (Russian), Matematicheskie Zametki , 49 (1991), N 1, 3-11, translated in Mathematical Notes of the Academy of Sciences of the USSR , 3-9, MR 92g:90129.

13. A.I. Barvinok, Calculation of exponential integrals (Russian), Zap. Nauchn. Sem. LOMI ,
192 , (1991), Teoriya Slozhnosti Vuchislenii N 5, 149-163, translated in Journal of Mathematical Sciences (New York), 70 (1994), No.4, MR 92i:65228.

14. A. Barvinok, Combinatorial complexity of orbits in representations of the symmetric group, Representation Theory and Dynamical Systems , ed. A.M. Vershik, Advances in Soviet Mathematics , 9 (1992), 161-182, MR 93k:20023.

15. A. Barvinok, On equivariant generalization of Dehn-Sommerville equations, Europ. J. Combinatorics , 13 (1992), 419-428, MR 93i:52016.

16. A.I. Barvinok, Exponential integrals and sums over convex polyhedra (Russian), Funktsional. Anal. i Prilozhen. , 26 (1992), N 2, 64-66, translated in Funct. Anal. Appl. , 127-129, MR 93g:32052.

17. A.I. Barvinok and V.P. Rozhkov, Intercentral coordination of cortical electrical processes during mental activity (Russian), Human Physiology, 18(3) (1992), 149-159.

18. A.I. Barvinok, Partition functions in optimization and computational problems, (Russian), Algebra i analiz , 4 (1992), N 1, 3-53, translated in St.-Petersburg Mathematical Journal , 1-49, MR 93f:90131.

19. A. Barvinok, Feasibility testing for systems of real quadratic equations, Discrete & Computational Geometry , 10 (1993), N 1, 1-13, MR 94f:14051.

20. A.I. Barvinok, A.M. Vershik and N.E. Mnev, The topology of configuration spaces, convex polytopes, and representations of lattices (Russian), Trudu Matem. Inst. Steklova , 193 (1992), translated in Proceedings of the Steklov Institute of Mathematics , 1993, issue 3, 37-41, MR 95e:52019

21. A. Barvinok, Computing the volume, counting integral points, and exponential sums, Discrete & Computational Geometry , 10 (1993), N 2, 123-141, MR 94d:52005.

22. A. Barvinok, Computing the Ehrhart polynomial of a convex lattice polytope, Discrete & Computational Geometry , 12 (1994), N 1, 35-48, MR 95e:52015.

23. A. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Mathematics of Operations Research , 19 (1994), 769-779, MR 96c:52026.

24. A. Barvinok, Problems of Distance Geometry and convex properties of quadratic maps, Discrete & Computational Geometry , 13 (1995), 189-202, MR 95k:51026.

25. A. Barvinok, New algorithms for linear k-matroid intersection and matroid k-parity problems, Mathematical Programming , 69 (1995), 449-470, MR 96j:05029.

26. A. Barvinok, Integral Geometry of higher-dimensional polytopes and the average case in combinatorial optimization, in: Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS'95) , IEEE Computer Society Press, 1995, 275-283.

27. A. Barvinok, Two algorithmic results for the Traveling Salesman Problem, Mathematics of Operations Research , 21 (1996), 65-84, MR 97a:90102.

28. A. Barvinok, On the Betti numbers of semialgebraic sets defined by few quadratic inequalities, Mathematische Zeitschrift , 225 (1997), 231-244, MR 98f:14044.

29. A. Barvinok, Lattice points and lattice polytopes, in: Handbook of Discrete and Computational Geometry , G.E. Goodman and J. O'Rourke, eds, CRC Press, Boca Raton, New York, 1997, 133-152.

30. A. Barvinok, Computing mixed discriminants, mixed volumes and permanents, Discrete & Computational Geometry , 18 (1997), 205-237, MR 98m:52011.

31. A. Barvinok and S.V. Fomin, Sparse interpolation of symmetric polynomials, Advances in Applied Mathematics , 18 (1997), 271-285, MR 98i:05164.

32. A. Barvinok, Approximate counting via random optimization, Random Structures & Algorithms , 11 (1997), 187-198, MR 98m:05009.

33. A. Barvinok, Measure concentration in optimization, Mathematical Programming, Ser. B , 79 (1997) (Lectures on Mathematical Programming, ISMP 97, T.M. Liebling and D. de Werra eds.), 33-53, MR 98h:90055.

34. A. Barvinok, Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor, Random Structures & Algorithms , 14 (1999), 29-61, MR 2000a:68044.

35. A. Barvinok, D. Johnson, G. Woeginger, and R. Woodroofe, The maximum Traveling Salesman Problem under polyhedral norms, Lecture Notes in Computer Science , 1412 (1998), 195--201, Springer-Verlag, Berlin-New York (Proceedings of the 6-th Conference on Integer Programming and Combinatorial Optimization (IPCO), R.E. Bixby, E.A. Boyd, and R.Z. Rios-Mercado, eds.), MR 2000j:90060.

36. A. Barvinok and J.E. Pommersheim, An algorithmic theory of lattice points in polyhedra, in: New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996-1997), 91-147, Math. Sci. Res. Inst. Publ. 38, Cambridge Univ. Press, Cambridge, 1999, MR 2000k:52014.

37. A. Barvinok, A remark on the rank of positive semidefinite matrices subject to affine constraints, Discrete & Computational Geometry , 25 (2001), 23-31, MR 2002i:90125.

38. A. Barvinok and A. Samorodnitsky, The distance approach to approximate combinatorial counting, Geometric and Functional Analysis, 11 (2001), 871-899, MR 2002i:60015.

39. A. Barvinok, E. Kh. Gimadi and A.I. Serdyukov, The maximum Traveling Salesman problem, in: The Traveling Salesman Problem and its Variations , 585-607, G. Gutin and A. Punnen, eds., Kluwer, 2002.

40. A. Barvinok, Estimating L- infinity norms by L2k norms for functions on orbits, Foundations of Computational Mathematics, 2 (2002), 393-412, MR 2003g:90056.

41. A. Barvinok, A Course in Convexity, Graduate Studies in Mathematics, vol. 54 , Amer. Math. Soc., Providence, RI, 2002, MR 2003j:52001.

42. A. Barvinok and T. Stephen, The distribution of values in the Quadratic Assignment Problem, Mathematics of Operations Research, 28 (2003), 64-91, MR 2004b:90077.

43. A. Barvinok, Approximating a norm by a polynomial, in: Geometric Aspects of Functional Analysis, Israel Seminar 2001-2002, V.D. Milman and G. Schechtman ed., Lecture Notes in Mathematics, 1807 (2003), 20-26, Springer-Verlag, Berlin-New York, MR 2005d:52009.

44. A. Barvinok and T. Stephen, On the distribution of values in the quadratic assignment problem, in: Novel Approaches to Hard Discrete Optimization, P. Pardalos and H. Wolkowicz, ed., Fields Institute Communications, 37 (2003), 1-16, Amer. Math. Soc., Providence, RI.

45. A. Barvinok and K. Woods, Short rational generating functions for lattice point problems, Journal of the American Mathematical Society, 16 (2003), 957-979, MR 2004e:05009.

46. A. Barvinok, S.P. Fekete, D.S. Johnson, A. Tamir, G.J. Woeginger and R. Woodroofe, The geometric maximum traveling salesman problem, Journal of the ACM, 50 (2003), 641-664, MR 2005m:68095.

47. A. Barvinok and G. Blekherman, Convex geometry of orbits, Combinatorial and Computational Geometry, MSRI Publications, 52 , 2005, 51-77, MR 2007a:52006.

48. A. Barvinok, Computing the Ehrhart quasi-polynomial of a rational simplex, Mathematics of Computation, 75 (2006), 1449--1466, MR 2007d:52020.

49. A. Barvinok, Approximating orthogonal matrices by permutation matrices, Pure and Applied Mathematics Quarterly, 2 (2006), 943--961, MR 2007h:52003.

50. A. Barvinok and A. Samorodnitsky, Random weighting, asymptotic counting, and inverse isoperimetry, Israel Journal of Mathematics, 158 (2007), 159-191.

51. A. Barvinok, Lattice points, polyhedra, and complexity, Geometric Combinatorics, IAS/Park City Mathematics Series, 13, 2007, 19--62.

52. A. Barvinok, Integration and optimization of multivariate polynomials by restriction onto a random subspace, Foundations of Computational Mathematics, 7 (2007), 229--244.

53. A. Barvinok, The complexity of generating functions for integer points in polyhedra and beyond, Proceedings of the International Congress of Mathematicians, Madrid, August 22-30, 2006 , European Mathematical Society, vol. 3, 763--787, MR 2007k:05007.

54. A. Barvinok, Brunn-Minkowski inequalities for contingency tables and integer flows, Advances in Mathematics, 211 (2007), 105--122, MR 2008c:05006.

55. A. Barvinok, Enumerating contingency tables via random permanents, Combinatorics, Probability and Computing, 17 (2008), 1--19.

56. A. Barvinok and E. Veomett, The computational complexity of convex bodies, Surveys on Discrete and Computational Geometry, Contemporary Mathematics, 453 (2008), 117--137.

57. A. Barvinok and I. Novik, A centrally symmetric version of the cyclic polytope, Discrete & Computational Geometry, 39 (2008), 76--99.

58. A. Barvinok, A. Samorodnitsky, and A. Yong, Counting magic squares in quasi-polynomial time, preprint math.CO/0703227, 2007.

59. A. Barvinok, Asymptotic estimates for the number of contingency tables, integer flows, and volumes of transportation polytopes, preprint arXiv:0709.3810, 2007.