Etingof, P.; Kalinov, D. et al. (2022) New realizations of deformed double current algebras and Deligne categories Transformation Groups; (In Press)
Albion, Seamus P.; Rains, Eric M. et al. (2021) AFLT-type Selberg integrals Communications in Mathematical Physics; Vol. 388; No. 2;
Nakamura, Akane; Rains, Eric (2021) Uniqueness of Polarization for the Autonomous 4-dimensional Painlevé-type Systems International Mathematics Research Notices; Vol. 2021; No. 18;
Etingof, Pavel; Klyuev, Daniil et al. (2021) Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 17;
Lee, Chul-hee; Rains, Eric M. et al. (2020) An Elliptic Hypergeometric Function Approach to Branching Rules Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 16;
Rains, Eric M. (2020) Elliptic Double Affine Hecke Algebras Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 16;
Rains, Eric M.; Warnaar, S. Ole (2018) A Nekrasov–Okounkov formula for Macdonald polynomials Journal of Algebraic Combinatorics; Vol. 48; No. 1;
Rains, Eric M.; Sam, Steven V. (2018) Invariant theory of ⋀^3(9) and genus 2 curves Algebra and Number Theory; Vol. 12; No. 4;
Jordan, Bruce W.; Keeton, Allan G. et al. (2018) Abelian varieties isogenous to a power of an elliptic curve Compositio Mathematica; Vol. 154; No. 5;
Rains, Eric M.; Sun, Yi et al. (2018) Affine Macdonald conjectures and special values of Felder–Varchenko functions Selecta Mathematica - New Series; Vol. 24; No. 2;
Rains, Eric M. (2018) Multivariate quadratic transformations and the interpolation kernel Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 14;
Ormerod, Chris M.; Rains, Eric M. (2017) An Elliptic Garnier System Communications in Mathematical Physics; Vol. 355; No. 2;
Ormerod, Christopher M.; Rains, Eric (2017) A symmetric difference-differential Lax pair for Painlevé VI Journal of Integrable Systems; Vol. 2; No. 1;
Ormerod, Christopher M.; Rains, Eric M. (2016) Commutation Relations and Discrete Garnier Systems Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 12;
Etingof, Pavel; Rains, Eric (2016) On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums Communications in Mathematical Physics; Vol. 347; No. 1;
Rains, Eric M. (2016) The noncommutative geometry of elliptic difference equations (Submitted)
Rains, Eric M.; Sam, Steven V. (2016) Vector bundles on genus 2 curves and trivectors (Submitted)
Okounkov, Andrei; Rains, Eric (2015) Noncommutative geometry and Painlevé equations Algebra and Number Theory; Vol. 9; No. 6;
Bhargava, Manjul; Kane, Daniel M. et al. (2015) Modeling the distribution of ranks, Selmer groups, and Shafarevich–Tate groups of elliptic curves Cambridge Journal of Mathematics; Vol. 3; No. 3;
Rains, Eric M.; Warnaar, S. Ole (2015) Bounded Littlewood identities (Submitted)
van de Bult, Fokko J.; Rains, Eric M. (2015) Limits of elliptic hypergeometric biorthogonal functions Journal of Approximation Theory; Vol. 193;
Rains, Eric M. (2013) Birational morphisms and Poisson moduli spaces (Submitted)
Rains, Eric M. (2013) Generalized Hitchin systems on rational surfaces (Submitted)
Rains, Eric; Ruijsenaars, Simon (2013) Difference Operators of Sklyanin and van Diejen Type Communications in Mathematical Physics; Vol. 320; No. 3;
Rains, Eric M.; Vazirani, Monica J. (2013) Deformations of permutation representations of Coxeter groups Journal of Algebraic Combinatorics; Vol. 37; No. 3;
Rains, Eric M. (2012) Elliptic Littlewood identities Journal of Combinatorial Theory. Series A; Vol. 119; No. 7;
Forrester, Peter J.; Rains, Eric M. (2012) A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals Communications in Mathematical Physics; Vol. 309; No. 3;
Poonen, Bjorn; Rains, Eric (2012) Random maximal isotropic subspaces and Selmer groups Journal of the American Mathematical Society; Vol. 25; No. 1;
van de Bult, Fokko J.; Rains, Eric M. (2011) Limits of multivariate elliptic beta integrals and related bilinear forms (Submitted)
van de Bult, Fokko J.; Rains, Eric M. (2011) Limits of multivariate elliptic hypergeometric biorthogonal functions (Submitted)
Rains, Eric M. (2011) An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 7;
Etingof, Pavel; Rains, Eric (2011) On Algebraically Integrable Differential Operators on an Elliptic Curve Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 7;
Rains, Eric M. (2011) Elliptic Analogues of the Macdonald and Koornwinder Polynomials Proceedings of the International Congress of Mathematicians : Hyderabad, August 19-27, 2010; 2010 International Congress of Mathematicians (ICM), 19-27 August 2010 , Hyderabad, India
Poonen, Bjorn; Rains, Eric (2011) Self cup products and the theta characteristic torsor Mathematical Research Letters; Vol. 18; No. 6;
Borodin, Alexei; Gorin, Vadim et al. (2010) q-Distributions on boxed plane partitions Selecta Mathematica - New Series; Vol. 16; No. 4;
Etingof, Pavel; Henriques, André et al. (2010) The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points Annals of Mathematics; Vol. 171; No. 2;
Rains, Eric M. (2010) Transformations of elliptic hypergeometric integrals Annals of Mathematics; Vol. 171; No. 1;
Rains, Eric M. (2010) The homology of real subspace arrangements Journal of Topology; Vol. 3; No. 4;
Rains, E. M.; Spiridonov, V. P. (2009) Determinants of elliptic hypergeometric integrals Functional Analysis and its Applications; Vol. 43; No. 4;
Forrester, Peter J.; Rains, Eric M. (2009) Matrix averages relating to Ginibre ensembles Journal of Physics A: Mathematical and Theoretical; Vol. 42; No. 38;
Lascoux, Alain; Rains, Eric M. et al. (2009) Nonsymmetric interpolation macdonald polynomials and gl_n basic hypergeometric series Transformation Groups; Vol. 14; No. 3;
van de Bult, Fokko J.; Rains, Eric M. (2009) Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 5; No. 059; Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions, 21-25 July 2008 , Bonn, Germany
Rains, Eric M. (2009) The action of S_n on the cohomology of M_(0,n)(R) Selecta Mathematica - New Series; Vol. 15; No. 1;
Rains, Eric M. (2009) Limits of elliptic hypergeometric integrals Ramanujan Journal; Vol. 18; No. 3;
Lagarias, Jeffrey C.; Rains, Eric et al. (2009) The Kruskal Count The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn;
Etingof, Pavel; Rains, Eric (2008) New Deformations of Group Algebras of Coxeter Groups, II Geometric and Functional Analysis; Vol. 17; No. 6;
Henderson, Anthony; Rains, Eric (2008) The cohomology of real De Concini–Procesi models of Coxeter type International Mathematics Research Notices; Vol. 2008;
Günther, Annika; Nebe, Gabriele et al. (2008) Clifford-Weil groups of quotient representations Albanian Journal of Mathematics; Vol. 2; No. 3;
Forrester, Peter J.; Rains, Eric M. (2007) Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths Journal of Statistical Physics; Vol. 129; No. 5-6;
Rains, Eric M.; Vazirani, Monica (2007) Vanishing Integrals of Macdonald and Koornwinder polynomials Transformation Groups; Vol. 12; No. 4;
van de Bult, F. J.; Rains, E. M. et al. (2007) Properties of Generalized Univariate Hypergeometric Functions Communications in Mathematical Physics; Vol. 275; No. 1;
Etingof, Pavel; Oblomkov, Alexei et al. (2007) Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces Advances in Mathematics; Vol. 212; No. 2;
Etingof, Pavel; Latour, Frédéric et al. (2007) On central extensions of preprojective algebras Journal of Algebra; Vol. 313; No. 1;
Bartholdi, Laurent; Enriquez, Benjamin et al. (2006) Groups and Lie algebras corresponding to the Yang–Baxter equations Journal of Algebra; Vol. 305; No. 2;
Heninger, Nadia; Rains, E. M. et al. (2006) On the integrality of nth roots of generating functions Journal of Combinatorial Theory. Series A; Vol. 113; No. 8;
Rains, Eric M.; Vazirani, Monica J. (2006) Quadratic transformations of Macdonald and Koornwinder polynomials (Submitted)
Etingof, Pavel; Rains, Eric (2006) Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups Journal of Algebra; Vol. 299; No. 2;
Forrester, Peter J.; Nagao, Taro et al. (2006) Correlation functions for random involutions International Mathematics Research Notices; Vol. 2006;
Forrester, Peter J.; Rains, Eric M. (2006) Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices International Mathematics Research Notices; Vol. 2006;
Rains, Eric M. (2006) A difference-integral representation of Koornwinder polynomials Jack, Hall-Littlewood and Macdonald Polynomials; Series.Contemporary Mathematics; No. 417; Workshop on Jack, Hall-Littlewood and Macdonald Polynomials, 2003 September 23-26 , Edinburgh, Scotland
Rains, Eric M. (2006) BC_n-symmetric abelian functions Duke Mathematical Journal; Vol. 135; No. 1;
Nebe, Gabriele; Rains, Eric M. et al. (2006) Self-Dual Codes and Invariant Theory Self-Dual Codes and Invariant Theory; Vol. 17; Series.Algorithms and Computation in Mathematics;
Borodin, Alexei; Rains, Eric M. (2005) Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs Journal of Statistical Physics; Vol. 121; No. 3-4;
Rains, Eric M. (2005) Recurrences for elliptic hypergeometric integrals (Submitted)
Rains, Eric M. (2005) BC_n-symmetric polynomials Transformation Groups; Vol. 10; No. 1;
Etingof, Pavel; Rains, Eric (2005) New deformations of group algebras of Coxeter groups International Mathematics Research Notices; Vol. 2005; No. 10;
Forrester, Peter J.; Rains, Eric M. (2005) Interpretations of some parameter dependent generalizations of classical matrix ensembles Probability Theory and Related Fields; Vol. 131; No. 1;
Lagarias, Jeffrey C.; Rains, Eric (2005) Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers Journal of Difference Equations and Applications; Vol. 11; No. 12;
Lagarias, Jeffrey C.; Rains, Eric (2005) Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles Journal of Difference Equations and Applications; Vol. 11; No. 13;
Lagarias, Jeffrey C.; Rains, Eric (2005) Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra Journal of Difference Equations and Applications; Vol. 11; No. 14;
Forrester, Peter J.; Rains, Eric M. (2004) Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter Probability Theory and Related Fields; Vol. 130; No. 4;
Nebe, G.; Rains, E. M. et al. (2004) Codes and invariant theory Mathematische Nachrichten; Vol. 274-275; No. 1;
Nebe, Gabriele; Quebbemann, H.-G. et al. (2004) Complete weight enumerators of generalized doubly-even self-dual codes Finite Fields and Their Applications; Vol. 10; No. 4;
Draper, Thomas G.; Kutin, Samuel A. et al. (2004) A logarithmic-depth quantum carry-lookahead adder (Submitted)
Quebbemann, H.-G.; Rains, E. M. (2003) On the involutions fixing the class of a lattice Journal of Number Theory; Vol. 101; No. 1;
Rains, Eric M. (2003) New asymptotic bounds for self-dual codes and lattices IEEE Transactions on Information Theory; Vol. 49; No. 5;
Applegate, David; Rains, E. M. et al. (2003) On asymmetric coverings and covering numbers Journal of Combinatorial Designs; Vol. 11; No. 3;
Rains, Eric M. (2003) Images of eigenvalue distributions under power maps Probability Theory and Related Fields; Vol. 125; No. 4;
Lagarias, Jeffrey C.; Rains, Eric (2003) On a two-variable zeta function for number fields Annales de l'Institut Fourier; Vol. 53; No. 1;
Rains, E. M.; Sloane, N. J. A. (2002) Self-Dual Codes (Submitted)
Rains, E. M.; Sloane, N. J. A. et al. (2002) The lattice of N-run orthogonal arrays Journal of Statistical Planning and Inference; Vol. 102; No. 2;
Lagarias, J. C.; Rains, E. M. et al. (2002) The EKG Sequence Experimental Mathematics; Vol. 11; No. 3;
Baik, Jinho; Deift, Percy et al. (2001) A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux Communications in Mathematical Physics; Vol. 223; No. 3;
Rains, Eric M. (2001) A semidefinite program for distillable entanglement IEEE Transactions on Information Theory; Vol. 47; No. 7;
Nebe, Gabriele; Rains, E. M. et al. (2001) The Invariants of the Clifford Groups Designs, Codes and Cryptography; Vol. 24; No. 1;
Rains, E. M. (2001) Class Groups and Modular Lattices Journal of Number Theory; Vol. 88; No. 2;
Baik, Jinho; Rains, Eric M. (2001) Algebraic aspects of increasing subsequences Duke Mathematical Journal; Vol. 109; No. 1;
Forrester, Peter J.; Rains, Eric M. (2001) Interrelationships Between Orthogonal, Unitary and Symplectic Matrix Ensembles Random Matrix Models and Their Applications; Series.Mathematical Sciences Research Institute publications ; No. 40;
Baik, Jinho; Rains, Eric M. (2001) Symmetrized Random Permutations Random Matrix Models and Their Applications; Series.Mathematical Sciences Research Institute publications ; No. 40;
Rains, Eric M.; Baik, Jinho (2001) The asymptotics of monotone subsequences of involutions Duke Mathematical Journal; Vol. 109; No. 2;
Baik, Jinho; Rains, Eric M. (2000) Limiting Distributions for a Polynuclear Growth Model with External Sources Journal of Statistical Physics; Vol. 100; No. 3-4;
Bonnecaze, A.; Rains, E. et al. (2000) 3-Colored 5-Designs and Z_4-Codes Journal of Statistical Planning and Inference; Vol. 86; No. 2;
Rains, Eric (2000) Bounds for Self-Dual Codes Over ℤ_4 Finite Fields and Their Applications; Vol. 6; No. 2;
Rains, Eric M. (2000) Polynomial invariants of quantum codes IEEE Transactions on Information Theory; Vol. 46; No. 1;
Odlyzko, A. M.; Rains, E. M. (2000) On longest increasing subsequences in random permutations Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis; Series.Contemporary Mathematics; No. 251;
Conway, J. H.; Rains, E. M. et al. (1999) On the Existence of Similar Sublattices Canadian Journal of Mathematics; Vol. 51; No. 6;
Rains, Eric M. (1999) Monotonicity of the quantum linear programming bound IEEE Transactions on Information Theory; Vol. 45; No. 7;
Rains, Eric M. (1999) Quantum shadow enumerators IEEE Transactions on Information Theory; Vol. 45; No. 7;
Rains, Eric M. (1999) Nonbinary quantum codes IEEE Transactions on Information Theory; Vol. 45; No. 6;
Rains, Eric (1999) Optimal self-dual codes over ℤ_4 Discrete Mathematics; Vol. 203; No. 1-3;
Calderbank, A. R.; Hardin, R. H. et al. (1999) A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces Journal of Algebraic Combinatorics; Vol. 9; No. 2;
Bennett, Charles H.; DiVincenzo, David P. et al. (1999) Quantum nonlocality without entanglement Physical Review A; Vol. 59; No. 2;
Rains, E. M.; Sloane, N. J. A. (1999) On Cayley's Enumeration of Alkanes (or 4-Valent Trees) Journal of Integer Sequences; Vol. 2;
Rains, Eric M. (1999) Quantum codes of minimum distance two IEEE Transactions on Information Theory; Vol. 45; No. 1;
Rains, E. M.; Sloane, N. J. A. (1998) The Shadow Theory of Modular and Unimodular Lattices Journal of Number Theory; Vol. 73; No. 2;
Rains, Eric M. (1998) Normal limit theorems for symmetric random matrices Probability Theory and Related Fields; Vol. 112; No. 3;
Calderbank, A. Robert; Rains, Eric M. et al. (1998) Quantum error correction via codes over GF(4) IEEE Transactions on Information Theory; Vol. 44; No. 4; 1997 IEEE International Symposium on Information Theory, June 29-July 4, 1997 , Ulm, Germany
Rains, Eric M. (1998) Quantum weight enumerators IEEE Transactions on Information Theory; Vol. 44; No. 4;
Lagarias, Jeffrey C.; Rains, Eric M. (1998) Rationals to and Only to Rationals: 10555 American Mathematical Monthly; Vol. 105; No. 3;
Rains, Eric M. (1998) Shadow bounds for self-dual codes IEEE Transactions on Information Theory; Vol. 44; No. 1;
Rains, E. M. (1998) Increasing Subsequences and the Classical Groups Electronic Journal of Combinatorics; Vol. 5;
Edel, Yves; Rains, E. M. et al. (1998) On Kissing Numbers in Dimensions 32 to 128 Electronic Journal of Combinatorics; Vol. 5;
Rains, E. M. (1997) Combinatorial Properties of Brownian Motion on the Compact Classical Groups Journal of Theoretical Probability; Vol. 10; No. 3;
Rains, E. M. (1997) High powers of random elements of compact Lie groups Probability Theory and Related Fields; Vol. 107; No. 2;
Calderbank, A. R.; Rains, E. M. et al. (1997) Quantum Error Correction and Orthogonal Geometry Physical Review Letters; Vol. 78; No. 3;
Robinson, Raphael M.; Goffinet, Daniel et al. (1996) Problems: 10550-10556 American Mathematical Monthly; Vol. 103; No. 9;
Brown, Robert W.; Rains, Eric M. et al. (1991) Harmonic analysis of the relativistic string in spinorial coordinates Classical and Quantum Gravity; Vol. 8; No. 7;