Computing the theta function
* Theory of Computing, * to appear

A quick estimate for the volume of a polyhedron
(with M. Rudelson)
* Israel Journal of Mathematics, * to appear

When a system of real quadratic equations has a solution
(with M. Rudelson)
* Advances in Mathematics, * **403** (2022), Article 108391

Smoothed counting of 0-1 points in polyhedra
* Random Structures & Algorithms, * ** 63 ** (2023), issue 1, 27--60

Testing systems of real quadratic equations for approximate solutions
* preprint *

More on zeros and approximation of the Ising partition function
(with N. Barvinok)
* Forum of Mathematics, Sigma, * **9**:e46 (2021), 1--18

A remark on approximating permanents of positive definite matrices
* Linear Algebra and its Applications, * ** 608 ** (2021), 399--406

Integrating products of quadratic forms
* Discrete & Computational Geometry, * to appear

Testing for dense subsets in a graph via the partition function
(with A. Della Pella)
* SIAM Journal on Discrete Mathematics, * **34** (2020), no. 1, 308--327

Approximating real-rooted and stable polynomials, with combinatorial applications
* Online Journal of Analytic Combinatorics, * **14** (2019), #08

Stability and complexity of mixed discriminants
* Mathematics of Computation, * **89** (2020), no. 322, 717--735

Computing permanents of complex diagonally dominant matrices and tensors
* Israel Journal of Mathematics, * **232** (2019), 931--945

Weighted counting of solutions to sparse systems of equations
(with G. Regts)
* Combinatorics, Probability and Computing, * **28** (2019), 696--719

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, * M. Loebl, J. Nešetřil and R. Thomas ed., 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 *L*^{2k} 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.