Rains, Eric

Article from CaltechAUTHORS

• Feng, Tony and Landesman, Aaron, et el. (2022) The geometric distribution of Selmer groups of elliptic curves over function fields; Mathematische Annalen; 10.1007/s00208-022-02429-1
• Etingof, P. and Kalinov, D., et el. (2022) New realizations of deformed double current algebras and Deligne categories; Transformation Groups; 10.1007/s00031-022-09717-9
• Albion, Seamus P. and Rains, Eric M., et el. (2021) AFLT-type Selberg integrals; Communications in Mathematical Physics; Vol. 388; No. 2; 735-791; 10.1007/s00220-021-04157-0
• Nakamura, Akane and Rains, Eric (2021) Uniqueness of Polarization for the Autonomous 4-dimensional Painlevé-type Systems; International Mathematics Research Notices; Vol. 2021; No. 18; 14204-14219; 10.1093/imrn/rnaa037
• Etingof, Pavel and Klyuev, Daniil, et el. (2021) Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A; Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 17; Art. No. 29; 10.3842/sigma.2021.029
• Lee, Chul-hee and Rains, Eric M., et el. (2020) An Elliptic Hypergeometric Function Approach to Branching Rules; Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 16; Art. No. 142; 10.3842/sigma.2020.142
• Rains, Eric M. (2020) Elliptic Double Affine Hecke Algebras; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 16; Art. No. 111; 10.3842/SIGMA.2020.111
• Rains, Eric M. and Warnaar, S. Ole (2018) A Nekrasov–Okounkov formula for Macdonald polynomials; Journal of Algebraic Combinatorics; Vol. 48; No. 1; 1-30; 10.1007/s10801-017-0790-2
• Rains, Eric M. and Sam, Steven V. (2018) Invariant theory of ⋀^3(9) and genus 2 curves; Algebra and Number Theory; Vol. 12; No. 4; 935-957; 10.2140/ant.2018.12.935
• Jordan, Bruce W. and Keeton, Allan G., et el. (2018) Abelian varieties isogenous to a power of an elliptic curve; Compositio Mathematica; Vol. 154; No. 5; 934-959; 10.1112/S0010437X17007990
• Rains, Eric M. and Sun, Yi, et el. (2018) Affine Macdonald conjectures and special values of Felder–Varchenko functions; Selecta Mathematica - New Series; Vol. 24; No. 2; 1549-1591; 10.1007/s00029-017-0328-4
• Rains, Eric M. (2018) Multivariate quadratic transformations and the interpolation kernel; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 14; Art. No. 019; 10.3842/SIGMA.2018.019
• Ormerod, Chris M. and Rains, Eric M. (2017) An Elliptic Garnier System; Communications in Mathematical Physics; Vol. 355; No. 2; 741-766; 10.1007/s00220-017-2934-6
• Ormerod, Christopher M. and Rains, Eric (2017) A symmetric difference-differential Lax pair for Painlevé VI; Journal of Integrable Systems; Vol. 2; No. 1; 1-20; 10.1093/integr/xyx003
• Ormerod, Christopher M. and Rains, Eric M. (2016) Commutation Relations and Discrete Garnier Systems; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 12; Art. No. 110; 10.3842/SIGMA.2016.110
• Etingof, Pavel and Rains, Eric (2016) On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums; Communications in Mathematical Physics; Vol. 347; No. 1; 163-182; 10.1007/s00220-016-2657-0
• Okounkov, Andrei and Rains, Eric (2015) Noncommutative geometry and Painlevé equations; Algebra and Number Theory; Vol. 9; No. 6; 1363-1400; 10.2140/ant.2015.9.1363
• Bhargava, Manjul and Kane, Daniel M., et el. (2015) Modeling the distribution of ranks, Selmer groups, and Shafarevich–Tate groups of elliptic curves; Cambridge Journal of Mathematics; Vol. 3; No. 3; 275-321; 10.4310/CJM.2015.v3.n3.a1
• van de Bult, Fokko J. and Rains, Eric M. (2015) Limits of elliptic hypergeometric biorthogonal functions; Journal of Approximation Theory; Vol. 193; 128-163; 10.1016/j.jat.2014.06.009
• Rains, Eric and Ruijsenaars, Simon (2013) Difference Operators of Sklyanin and van Diejen Type; Communications in Mathematical Physics; Vol. 320; No. 3; 851-889; 10.1007/s00220-013-1692-3
• Rains, Eric M. and Vazirani, Monica J. (2013) Deformations of permutation representations of Coxeter groups; Journal of Algebraic Combinatorics; Vol. 37; No. 3; 455-502; 10.1007/s10801-012-0371-3
• Rains, Eric M. (2012) Elliptic Littlewood identities; Journal of Combinatorial Theory. Series A; Vol. 119; No. 7; 1558-1609; 10.1016/j.jcta.2012.03.001
• Forrester, Peter J. and Rains, Eric M. (2012) A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals; Communications in Mathematical Physics; Vol. 309; No. 3; 771-792; 10.1007/s00220-011-1305-y
• Poonen, Bjorn and Rains, Eric (2012) Random maximal isotropic subspaces and Selmer groups; Journal of the American Mathematical Society; Vol. 25; No. 1; 245-269; 10.1090/S0894-0347-2011-00710-8
• 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; Art. No. 088; 10.3842/SIGMA.2011.088
• Etingof, Pavel and Rains, Eric (2011) On Algebraically Integrable Differential Operators on an Elliptic Curve; Symmetry, Integrability and Geometry, Methods and Applications (SIGMA); Vol. 7; Art. No. 62; 10.3842/SIGMA.2011.062
• Poonen, Bjorn and Rains, Eric (2011) Self cup products and the theta characteristic torsor; Mathematical Research Letters; Vol. 18; No. 6; 1305-1318; 10.4310/MRL.2011.v18.n6.a18
• Borodin, Alexei and Gorin, Vadim, et el. (2010) q-Distributions on boxed plane partitions; Selecta Mathematica - New Series; Vol. 16; No. 4; 731-789; 10.1007/s00029-010-0034-y
• Etingof, Pavel and Henriques, André, et el. (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; 731-777; 10.4007/annals.2010.171.731
• Rains, Eric M. (2010) Transformations of elliptic hypergeometric integrals; Annals of Mathematics; Vol. 171; No. 1; 169-243; 10.4007/annals.2010.171.169
• Rains, Eric M. (2010) The homology of real subspace arrangements; Journal of Topology; Vol. 3; No. 4; 786-818; 10.1112/jtopol/jtq027
• Rains, E. M. and Spiridonov, V. P. (2009) Determinants of elliptic hypergeometric integrals; Functional Analysis and its Applications; Vol. 43; No. 4; 297-311; 10.1007/s10688-009-0037-7
• Forrester, Peter J. and Rains, Eric M. (2009) Matrix averages relating to Ginibre ensembles; Journal of Physics A: Mathematical and Theoretical; Vol. 42; No. 38; Art. No. 385205; 10.1088/1751-8113/42/38/385205
• Lascoux, Alain and Rains, Eric M., et el. (2009) Nonsymmetric interpolation macdonald polynomials and gl_n basic hypergeometric series; Transformation Groups; Vol. 14; No. 3; 613-647; 10.1007/s00031-009-9061-1
• van de Bult, Fokko J. and 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; 10.3842/SIGMA.2009.059
• 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; 171-188; 10.1007/s00029-008-0467-8
• Rains, Eric M. (2009) Limits of elliptic hypergeometric integrals; Ramanujan Journal; Vol. 18; No. 3; 257-306; 10.1007/s11139-007-9055-3
• Etingof, Pavel and Rains, Eric (2008) New Deformations of Group Algebras of Coxeter Groups, II; Geometric and Functional Analysis; Vol. 17; No. 6; 1851-1871; 10.1007/s00039-007-0642-7
• Henderson, Anthony and Rains, Eric (2008) The cohomology of real De Concini–Procesi models of Coxeter type; International Mathematics Research Notices; Vol. 2008; Art. No. rnn001; 10.1093/imrn/rnn001
• Günther, Annika and Nebe, Gabriele, et el. (2008) Clifford-Weil groups of quotient representations; Albanian Journal of Mathematics; Vol. 2; No. 3; 159-169
• Forrester, Peter J. and Rains, Eric M. (2007) Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths; Journal of Statistical Physics; Vol. 129; No. 5-6; 833-855; 10.1007/s10955-007-9413-y
• Rains, Eric M. and Vazirani, Monica (2007) Vanishing Integrals of Macdonald and Koornwinder polynomials; Transformation Groups; Vol. 12; No. 4; 725-759; 10.1007/S00031-007-0058-3
• van de Bult, F. J. and Rains, E. M., et el. (2007) Properties of Generalized Univariate Hypergeometric Functions; Communications in Mathematical Physics; Vol. 275; No. 1; 37-95; 10.1007/s00220-007-0289-0
• Etingof, Pavel and Oblomkov, Alexei, et el. (2007) Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces; Advances in Mathematics; Vol. 212; No. 2; 749-796; 10.1016/j.aim.2006.11.008
• Etingof, Pavel and Latour, Frédéric, et el. (2007) On central extensions of preprojective algebras; Journal of Algebra; Vol. 313; No. 1; 165-175; 10.1016/j.jalgebra.2006.11.040
• Bartholdi, Laurent and Enriquez, Benjamin, et el. (2006) Groups and Lie algebras corresponding to the Yang–Baxter equations; Journal of Algebra; Vol. 305; No. 2; 742-764; 10.1016/j.jalgebra.2005.12.006
• Heninger, Nadia and Rains, E. M., et el. (2006) On the integrality of nth roots of generating functions; Journal of Combinatorial Theory. Series A; Vol. 113; No. 8; 1732-1745; 10.1016/j.jcta.2006.03.018
• Etingof, Pavel and 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; 570-588; 10.1016/j.jalgebra.2006.01.005
• Forrester, Peter J. and Rains, Eric M. (2006) Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices; International Mathematics Research Notices; Vol. 2006; Art. No. 48306; 10.1155/IMRN/2006/48306
• Forrester, Peter J. and Nagao, Taro, et el. (2006) Correlation functions for random involutions; International Mathematics Research Notices; Vol. 2006; Art. No. 89796; 10.1155/IMRN/2006/89796
• Rains, Eric M. (2006) BC_n-symmetric abelian functions; Duke Mathematical Journal; Vol. 135; No. 1; 99-180; 10.48550/arXiv.0402113
• Borodin, Alexei and Rains, Eric M. (2005) Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs; Journal of Statistical Physics; Vol. 121; No. 3-4; 291-317; 10.1007/s10955-005-7583-z
• Rains, Eric M. (2005) BC_n-symmetric polynomials; Transformation Groups; Vol. 10; No. 1; 63-132; 10.1007/s00031-005-1003-y
• Etingof, Pavel and Rains, Eric (2005) New deformations of group algebras of Coxeter groups; International Mathematics Research Notices; Vol. 2005; No. 10; 635-646; 10.1155/IMRN.2005.635
• Forrester, Peter J. and Rains, Eric M. (2005) Interpretations of some parameter dependent generalizations of classical matrix ensembles; Probability Theory and Related Fields; Vol. 131; No. 1; 1-61; 10.1007/s00440-004-0375-6
• Lagarias, Jeffrey C. and 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; 1137-1163; 10.1080/10236190500273127
• Lagarias, Jeffrey C. and 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; 1205-1224; 10.1080/10236190500273184
• Lagarias, Jeffrey C. and 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; 1089-1108; 10.1080/10236190500273069
• Forrester, Peter J. and 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; 518-576; 10.1007/s00440-004-0374-7
• Nebe, G. and Rains, E. M., et el. (2004) Codes and invariant theory; Mathematische Nachrichten; Vol. 274-275; No. 1; 104-116; 10.1002/mana.200310204
• Nebe, Gabriele and Quebbemann, H.-G., et el. (2004) Complete weight enumerators of generalized doubly-even self-dual codes; Finite Fields and Their Applications; Vol. 10; No. 4; 540-550; 10.1016/j.ffa.2003.12.001
• Quebbemann, H.-G. and Rains, E. M. (2003) On the involutions fixing the class of a lattice; Journal of Number Theory; Vol. 101; No. 1; 185-194; 10.1016/S0022-314X(03)00022-2
• Rains, Eric M. (2003) New asymptotic bounds for self-dual codes and lattices; IEEE Transactions on Information Theory; Vol. 49; No. 5; 1261-1274; 10.1109/TIT.2003.810623
• Applegate, David and Rains, E. M., et el. (2003) On asymmetric coverings and covering numbers; Journal of Combinatorial Designs; Vol. 11; No. 3; 218-228; 10.1002/jcd.10022
• Rains, Eric M. (2003) Images of eigenvalue distributions under power maps; Probability Theory and Related Fields; Vol. 125; No. 4; 522-538; 10.1007/s00440-002-0250-2
• Lagarias, Jeffrey C. and Rains, Eric (2003) On a two-variable zeta function for number fields; Annales de l'Institut Fourier; Vol. 53; No. 1; 1-68
• Rains, E. M. and Sloane, N. J. A., et el. (2002) The lattice of N-run orthogonal arrays; Journal of Statistical Planning and Inference; Vol. 102; No. 2; 477-500; 10.1016/S0378-3758(01)00119-7
• Lagarias, J. C. and Rains, E. M., et el. (2002) The EKG Sequence; Experimental Mathematics; Vol. 11; No. 3; 437-446; 10.1080/10586458.2002.10504486
• Rains, Eric M. (2001) A semidefinite program for distillable entanglement; IEEE Transactions on Information Theory; Vol. 47; No. 7; 2921-2933; 10.1109/18.959270
• Baik, Jinho and Deift, Percy, et el. (2001) A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux; Communications in Mathematical Physics; Vol. 223; No. 3; 627-672; 10.1007/s002200100555
• Nebe, Gabriele and Rains, E. M., et el. (2001) The Invariants of the Clifford Groups; Designs, Codes and Cryptography; Vol. 24; No. 1; 99-122; 10.1023/A:1011233615437
• Rains, E. M. (2001) Class Groups and Modular Lattices; Journal of Number Theory; Vol. 88; No. 2; 211-224; 10.1006/jnth.2000.2633
• Baik, Jinho and Rains, Eric M. (2001) Algebraic aspects of increasing subsequences; Duke Mathematical Journal; Vol. 109; No. 1; 1-65; 10.1215/S0012-7094-01-10911-3
• Rains, Eric M. and Baik, Jinho (2001) The asymptotics of monotone subsequences of involutions; Duke Mathematical Journal; Vol. 109; No. 2; 205-281; 10.1215/S0012-7094-01-10921-6
• Baik, Jinho and Rains, Eric M. (2000) Limiting Distributions for a Polynuclear Growth Model with External Sources; Journal of Statistical Physics; Vol. 100; No. 3-4; 523-541; 10.1023/A:1018615306992
• Bonnecaze, A. and Rains, E., et el. (2000) 3-Colored 5-Designs and Z_4-Codes; Journal of Statistical Planning and Inference; Vol. 86; No. 2; 349-368; 10.1016/S0378-3758(99)00117-2
• Rains, Eric (2000) Bounds for Self-Dual Codes Over ℤ_4; Finite Fields and Their Applications; Vol. 6; No. 2; 146-163; 10.1006/ffta.1999.0258
• Rains, Eric M. (2000) Polynomial invariants of quantum codes; IEEE Transactions on Information Theory; Vol. 46; No. 1; 54-59; 10.1109/18.817508
• Conway, J. H. and Rains, E. M., et el. (1999) On the Existence of Similar Sublattices; Canadian Journal of Mathematics; Vol. 51; No. 6; 1300-1306; 10.4153/CJM-1999-059-5
• Rains, Eric M. (1999) Monotonicity of the quantum linear programming bound; IEEE Transactions on Information Theory; Vol. 45; No. 7; 2489-2492; 10.1109/18.796387
• Rains, Eric M. (1999) Quantum shadow enumerators; IEEE Transactions on Information Theory; Vol. 45; No. 7; 2361-2366; 10.1109/18.796376
• Rains, Eric M. (1999) Nonbinary quantum codes; IEEE Transactions on Information Theory; Vol. 45; No. 6; 1827-1832; 10.1109/18.782103
• Rains, Eric (1999) Optimal self-dual codes over ℤ_4; Discrete Mathematics; Vol. 203; No. 1-3; 215-228; 10.1016/S0012-365X(98)00358-6
• Calderbank, A. R. and Hardin, R. H., et el. (1999) A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces; Journal of Algebraic Combinatorics; Vol. 9; No. 2; 129-140; 10.1023/A:1018673825179
• Bennett, Charles H. and DiVincenzo, David P., et el. (1999) Quantum nonlocality without entanglement; Physical Review A; Vol. 59; No. 2; 1070-1091; 10.1103/PhysRevA.59.1070
• Rains, E. M. and Sloane, N. J. A. (1999) On Cayley's Enumeration of Alkanes (or 4-Valent Trees); Journal of Integer Sequences; Vol. 2; Art. No. 99.1.1; 10.48550/arXiv.0207176
• Rains, Eric M. (1999) Quantum codes of minimum distance two; IEEE Transactions on Information Theory; Vol. 45; No. 1; 266-271; 10.1109/18.746807
• Rains, E. M. and Sloane, N. J. A. (1998) The Shadow Theory of Modular and Unimodular Lattices; Journal of Number Theory; Vol. 73; No. 2; 359-389; 10.1006/jnth.1998.2306
• Rains, Eric M. (1998) Normal limit theorems for symmetric random matrices; Probability Theory and Related Fields; Vol. 112; No. 3; 411-423; 10.1007/s004400050195
• Calderbank, A. Robert and Rains, Eric M., et el. (1998) Quantum error correction via codes over GF(4); IEEE Transactions on Information Theory; Vol. 44; No. 4; 1369-1387; 10.1109/18.681315
• Rains, Eric M. (1998) Quantum weight enumerators; IEEE Transactions on Information Theory; Vol. 44; No. 4; 1388-1394; 10.1109/18.681316
• Lagarias, Jeffrey C. and Rains, Eric M. (1998) Rationals to and Only to Rationals: 10555; American Mathematical Monthly; Vol. 105; No. 3; 277-278
• Rains, Eric M. (1998) Shadow bounds for self-dual codes; IEEE Transactions on Information Theory; Vol. 44; No. 1; 134-139; 10.1109/18.651000
• Rains, E. M. (1998) Increasing Subsequences and the Classical Groups; Electronic Journal of Combinatorics; Vol. 5; Art. No. R12
• Edel, Yves and Rains, E. M., et el. (1998) On Kissing Numbers in Dimensions 32 to 128; Electronic Journal of Combinatorics; Vol. 5; Art. No. R22
• Rains, E. M. (1997) Combinatorial Properties of Brownian Motion on the Compact Classical Groups; Journal of Theoretical Probability; Vol. 10; No. 3; 659-679; 10.1023/A:1022601711176
• Rains, E. M. (1997) High powers of random elements of compact Lie groups; Probability Theory and Related Fields; Vol. 107; No. 2; 219-241; 10.1007/s004400050084
• Calderbank, A. R. and Rains, E. M., et el. (1997) Quantum Error Correction and Orthogonal Geometry; Physical Review Letters; Vol. 78; No. 3; 405-408; 10.1103/PhysRevLett.78.405
• Robinson, Raphael M. and Goffinet, Daniel, et el. (1996) Problems: 10550-10556; American Mathematical Monthly; Vol. 103; No. 9; 808-809; 10.2307/2974454
• Brown, Robert W. and Rains, Eric M., et el. (1991) Harmonic analysis of the relativistic string in spinorial coordinates; Classical and Quantum Gravity; Vol. 8; No. 7; 1245-1253; 10.1088/0264-9381/8/7/003