• Weighted counting of non-negative integer points in a subspace
  • (with G. Regts)

    preprint

  • Approximating permanents and hafnians
  • Discrete Analysis, 2017:2, 34 pp.

  • Concentration of the mixed discriminant of well-conditioned matrices
  • Linear Algebra and its Applications, 493 (2016), 120--133

  • Computing the partition function of a polynomial on the Boolean cube
  • A Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek, edited by M. Loebl, J. Nešetřil and R. Thomas, Springer 2017, 135--164

  • Computing the partition function for graph homomorphisms with multiplicities
  • (with P. Soberon)

    Journal of Combinatorial Theory, Series A, 137 (2016), 1--26

  • Computing the partition function for graph homomorphisms
  • (with P. Soberon)

    Combinatorica, 37 (2017), 633--650

  • Computing the partition function for cliques in a graph
  • Theory of Computing, 11 (2015), Article 13, 339--355

  • Computing the permanent of (some) complex matrices
  • Foundations of Computational Mathematics, 16 (2016), Issue 2, 329--342

  • On testing Hamiltonicity of graphs
  • Discrete Mathematics, 338 (2015), 53--58

  • Convexity of the image of a quadratic map via the relative entropy distance
  • Beiträge zur Algebra und Geometrie, 55 (2014), 577--593

  • Thrifty approximations of convex bodies by polytopes
  • International Mathematics Research Notices, 2014 (2014), 4341--4356

  • Approximations of convex bodies by polytopes and by projections of spectrahedra
  • preprint

  • Explicit constructions of centrally symmetric k-neighborly polytopes and large strictly antipodal sets
  • (with S.J. Lee and I. Novik)

    Discrete & Computational Geometry, 49 (2013), 429--443

  • A bound for the number of vertices of a polytope with applications
  • Combinatorica, 33 (2013), 1--10

  • Centrally symmetric polytopes with many faces
  • (with S.J. Lee and I. Novik)

    Israel Journal of Mathematics, 195 (2013), 457--472

  • Neighborliness of the symmetric moment curve
  • (with S.J. Lee and I. Novik)

    Mathematika, 59 (2013), 223--249

  • Matrices with prescribed row and column sums
  • Linear Algebra and its Applications, 436 (2012), 820--844

  • Computing the partition function for perfect matchings in a hypergraph
  • (with A. Samorodnitsky)

    Combinatorics, Probability and Computing, 20 (2011), 815--825

  • The number of graphs and a random graph with a given degree sequence
  • (with J.A. Hartigan)

    Random Structures & Algorithms, 42 (2013), 301--348

  • An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums
  • (with J.A. Hartigan)

    Transactions of the American Mathematical Society, 364 (2012), 4323--4368

  • Maximum entropy Gaussian approximation for the number of integer points and volumes of polytopes
  • (with J.A. Hartigan)

    Advances in Applied Mathematics, 45 (2010), 252--289

  • What does a random contingency table look like?
  • Combinatorics, Probability and Computing, 19 (2010), 517--539

  • On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries
  • Advances in Mathematics, 224 (2010), 316--339

  • An approximation algorithm for counting contingency tables
  • (with Z. Luria, A. Samorodnitsky and A. Yong)

    Random Structures & Algorithms, 37 (2010), 25--66

  • Asymptotic estimates for the number of contingency tables, integer flows, and volumes of transportation polytopes
  • International Mathematics Research Notices, 2009 (2009), No. 2, 348--385

  • A centrally symmetric version of the cyclic polytope
  • (with I. Novik)

    Discrete & Computational Geometry, 39 (2008), 76--99

  • The computational complexity of convex bodies
  • (with E. Veomett)

    Surveys on Discrete and Computational Geometry, Contemporary Mathematics, 453 (2008), 117--137

  • Brunn-Minkowski inequalities for contingency tables and integer flows
  • Advances in Mathematics, 211 (2007), 105--122

  • 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.

  • Enumerating contingency tables via random permanents
  • Combinatorics, Probability and Computing, 17 (2008), 1--19

  • Approximating orthogonal matrices by permutation matrices
  • Pure and Applied Mathematics Quarterly, 2 (2006), N 2, 943--961

  • Computing the Ehrhart quasi-polynomial of a rational simplex
  • Mathematics of Computation, 75 (2006), 1449-1466

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

  • Lattice points, polyhedra, and complexity
  • Geometric Combinatorics, IAS/Park City Mathematics Series, 13, 2007, 19-62

  • Convex geometry of orbits
  • (with G. Blekherman)

    Combinatorial and Computational Geometry, MSRI Publications, 52, 2005, 51-77

  • C++ codes for estimating permanents, hafnians and the number of forests in a graph
  • These codes, written by Alexander Yong, implement the algorithm suggested in the paper ``Random weighting ...'' below

  • Random weighting, asymptotic counting, and inverse isoperimetry
  • (with A. Samorodnitsky)

    Israel Journal of Mathematics, 158(2007), 159-191.

  • Short rational generating functions for lattice point problems
  • (with K. Woods)

    Journal of the American Mathematical Society, 16(2003), 957-979.

  • Estimating L-infinity norms by L2k norms for functions on orbits
  • Foundations of Computational Mathematics, 2(2002), 393-412.

  • 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.

  • The distribution of values in the Quadratic Assignment Problem
  • (with T. Stephen)

    Mathematics of Operations Research, 28(2003), 64-91.

  • The Maximum Traveling Salesman Problem
  • (with E.Kh. Gimadi and A.I. Serdyukov)

    in: The Traveling Salesman problem and its variations , 585-607, G. Gutin and A. Punnen, eds., Kluwer, 2002.

  • New Permanent Estimators via Non-Commutative Determinants
  • preprint

  • A C++ code to compute bounds for the permanent of a 0-1 matrix by the ``average distance'' approach
  • This code, written by Eric Michael Ryckman, is a realization of the algorithm suggested in the paper ``The distance approach ...'' below.

  • The distance approach to approximate combinatorial counting
  • (with A. Samorodnitsky)

    Geometric and Functional Analysis, 11(2001), 871-899.

  • A remark on the rank of positive semidefinite matrices subject to affine constraints
  • Discrete & Computational Geometry, 25(2001), 23-31.

  • Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor
  • Random Structures & Algorithms, 14(1999), 29-61.

  • Finding maximum length tours under polyhedral norms
  • (with D. Johnson, G. Woeginger, and R. Woodroofe)

    Lecture Notes in Computer Science, 1412(1998), 195-201.

  • An algorithmic theory of lattice points in polyhedra
  • (with J. Pommersheim)

    New Perspectives in Algebraic Combinatorics, MSRI Publications, 38, 1999, 91-147.