Eric M. Rains | Academic Influence

Eric M. Rains's AcademicInfluence.com Rankings

Eric M. Rains

Mathematics

#6333

World Rank

#8793

Historical Rank

Number Theory

#235

World Rank

#300

Historical Rank

Algebra

#341

World Rank

#473

Historical Rank

Measure Theory

#2199

World Rank

#2645

Historical Rank

mathematics Degrees

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Mathematics

Eric M. Rains's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Eric M. Rains Influential?

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According to Wikipedia, Eric Michael Rains is an American mathematician specializing in coding theory and special functions, especially applications from and to noncommutative algebraic geometry. Biography Eric Rains was 14 when he began classes in 1987. He left Case Western Reserve University with bachelor's degrees in computer science and physics and a master's degree in mathematics at age 17.

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Eric M. Rains's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Quantum error correction via codes over GF(4) (1996) (1546)
Quantum nonlocality without entanglement (1998) (813)
Quantum Error Correction and Orthogonal Geometry (1996) (677)
Nonbinary quantum codes (1997) (339)
A semidefinite program for distillable entanglement (2000) (271)
Limiting Distributions for a Polynuclear Growth Model with External Sources (2000) (263)
Shadow Bounds for Self-Dual Codes (1998) (252)
Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs (2004) (248)
A logarithmic-depth quantum carry-lookahead adder (2004) (236)
Bound on distillable entanglement (1998) (226)
Algebraic aspects of increasing subsequences (1999) (210)
Self-Dual Codes (2002) (200)
The asymptotics of monotone subsequences of involutions (1999) (191)
Quantum Error Correction Via Codes Over GF (1998) (187)
Transformations of elliptic hypergeometric integrals (2010) (184)
RIGOROUS TREATMENT OF DISTILLABLE ENTANGLEMENT (1998) (157)
Symmetrized Random Permutations (1999) (144)
Increasing Subsequences and the Classical Groups (1998) (135)
The Invariants of the Clifford Groups (2000) (118)
Interpretations of some parameter dependent generalizations of classical matrix ensembles (2002) (114)
Correlation functions for symmetrized increasing subsequences (2000) (111)
$BC_n$-symmetric abelian functions (2004) (101)
q-Distributions on boxed plane partitions (2009) (98)
Quantum Weight Enumerators (1996) (97)
The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points (2005) (96)
A nonadditive quantum code (1997) (95)
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces (1999) (92)
The Shadow Theory of Modular and Unimodular Lattices (1998) (92)
Random maximal isotropic subspaces and Selmer groups (2010) (90)
Polynomial invariants of quantum codes (1997) (81)
BCn-symmetric polynomials (2005) (81)
Limits of elliptic hypergeometric integrals (2006) (77)
Quantum shadow enumerators (1996) (77)
High powers of random elements of compact Lie groups (1997) (72)
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves (2013) (71)
Quantum Codes of Minimum Distance Two (1997) (67)
On the Existence of Similar Sublattices (1999) (66)
Entanglement purification via separable superoperators (1997) (66)
Interrelationships between orthogonal, unitary and symplectic matrix ensembles (1999) (65)
Combinatorial Properties of Brownian Motion on the Compact Classical Groups (1997) (59)
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics) (2006) (53)
Optimal self-dual codes over Z4 (1999) (53)
Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces (2004) (48)
Transformations of elliptic hypergometric integrals (2003) (46)
Groups and Lie algebras corresponding to the Yang–Baxter equations (2005) (45)
Properties of Generalized Univariate Hypergeometric Functions (2006) (44)
On Longest Increasing Subsequences in Random Permutations (1998) (43)
A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux (2000) (42)
Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter (2002) (38)
Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices (2005) (37)
3-Colored 5-Designs and Z4-Codes (2000) (34)
Images of eigenvalue distributions under power maps (2000) (32)
Bounded Littlewood identities (2015) (31)
Deformations of permutation representations of Coxeter groups (2010) (30)
Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups (2005) (28)
On a two-variable zeta function for number fields (2001) (26)
Multivariate Quadratic Transformations and the Interpolation Kernel (2014) (26)
Recurrences for elliptic hypergeometric integrals (2005) (23)
An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) (2008) (23)
New Deformations of Group Algebras of Coxeter Groups, II (2004) (23)
Matrix averages relating to Ginibre ensembles (2009) (23)
The homology of real subspace arrangements (2006) (22)
Vanishing Integrals of Macdonald and Koornwinder polynomials (2007) (22)
Self cup products and the theta characteristic torsor (2011) (21)
Abelian varieties isogenous to a power of an elliptic curve (2016) (21)
A mean identity for longest increasing subsequence problems (2000) (20)
Elliptic Littlewood identities (2008) (20)
On Cayley's Enumeration of Alkanes (or 4-Valent Trees) (2002) (19)
A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals (2010) (19)
Erratum: Bound on distillable entanglement [Phys. Rev. A 60, 179 (1999)] (2000) (19)
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions (2009) (19)
Determinants of elliptic hypergeometric integrals (2007) (19)
On asymmetric coverings and covering numbers (2002) (19)
A Simple Construction for the Barnes-Wall Lattices (2002) (18)
Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles (2003) (18)
Difference Operators of Sklyanin and van Diejen Type (2012) (17)
Bounds for Self-Dual Codes Over Z4 (2000) (16)
Complete weight enumerators of generalized doubly-even self-dual codes (2003) (16)
Commutation Relations and Discrete Garnier Systems (2016) (16)
Nonsymmetric interpolation macdonald polynomials and $ \mathfrak{g}\mathfrak{l}_n $ basic hypergeometric series (2009) (15)
Correlation functions for random involutions (2005) (15)
On the integrality of nth roots of generating functions (2005) (14)
Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers (2003) (13)
Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths (2007) (13)
Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra (2005) (13)
Codes and invariant theory (2003) (13)
Monotonicity of the quantum linear programming bound (1998) (12)
New asymptotic bounds for self-dual codes and lattices (2001) (12)
Generalized Hitchin systems on rational surfaces (2013) (12)
Nonsymmetric interpolation Macdonald polynomials and g_n basic hypergeometric series (2008) (12)
A Nekrasov–Okounkov formula for Macdonald polynomials (2016) (11)
On Kissing Numbers in Dimensions 32 to 128 (1998) (11)
THE ACTION OF Sn ON THE COHOMOLOGY OF M0,n(R) (2006) (11)
On central extensions of preprojective algebras (2006) (10)
The lattice of N-run orthogonal arrays (2002) (10)
On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums (2015) (9)
Limits of elliptic hypergeometric biorthogonal functions (2011) (9)
Noncommutative geometry and Painlevé equations (2014) (8)
The noncommutative geometry of elliptic difference equations (2016) (8)
BC_n-symmetric polynomials (2001) (8)
Normal limit theorems for symmetric random matrices (1998) (8)
Elliptic Double Affine Hecke Algebras (2017) (8)
The Cohomology of Real De Concini–Procesi Models of Coxeter Type (2006) (8)
The Kruskal Count (2001) (8)
An Elliptic Garnier System (2016) (7)
The EKG Sequence (2002) (7)
AFLT-type Selberg integrals (2020) (7)
The action of Sn on the cohomology of $$\overline{M}_{0,n}(\mathbb{R})$$ (2009) (7)
Limits of multivariate elliptic hypergeometric biorthogonal functions (2011) (7)
Invariant theory of ∧3(9) and genus-2 curves (2017) (7)
On Algebraically Integrable Differential Operators on an Elliptic Curve (2010) (7)
Last update: April 3rd, 2014 ERRATUM AND COMPLEMENTS TO MONOGRAPHIE 37 RÉSEAUX EUCLIDIENS, DESIGNS SPHÉRIQUES ET FORMES MODULAIRES (2014) (6)
NEW REALIZATIONS OF DEFORMED DOUBLE CURRENT ALGEBRAS AND DELIGNE CATEGORIES (2020) (6)
A difference-integral representation of Koornwinder polynomials (2004) (6)
A symmetric difference-differential Lax pair for Painlev\'e VI (2016) (6)
Limits of multivariate elliptic beta integrals and related bilinear forms (2011) (6)
Mittag-Leffler type sums associated with root systems (2018) (5)
J an 2 00 6 BC n-symmetric abelian functions (2008) (5)
ORTHOGONALITY OF VERY WELL-POISED SERIES (2015) (5)
Birational morphisms and Poisson moduli spaces (2013) (5)
Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A (2020) (4)
Measuring the roughness of interfaces (1991) (4)
An Elliptic Hypergeometric Function Approach to Branching Rules (2020) (4)
An isomonodromy interpretation of the elliptic Painlev\'e equation. I (2008) (4)
The action of S n on the cohomology of (2006) (3)
Clifford-Weil groups of quotient representations (2008) (3)
The geometric distribution of Selmer groups of elliptic curves over function fields (2020) (3)
Harmonic analysis of the relativistic string in spinorial coordinates (1991) (2)
On Longest Increasing Subsequences in Random Permutations on Longest Increasing Subsequences in Random Permutations (1998) (2)
Real and Complex Clifford Groups (2006) (2)
Affine Macdonald conjectures and special values of Felder–Varchenko functions (2016) (2)
Vector bundles on genus 2 curves and trivectors (2016) (2)
Elliptic Analogues of the Macdonald and Koornwinder Polynomials (2011) (2)
Quadratic transformations of Macdonald and Koornwinder polynomials (2006) (2)
The birational geometry of noncommutative surfaces. (2019) (1)
Hyperelliptic limits of quadrics through canonical curves and ribbons (2019) (1)
Class Groups and Modular Lattices (2001) (1)
9 Ju n 20 06 QUADRATIC TRANSFORMATIONS OF MACDONALD AND KOORNWINDER (2008) (0)
A ] 7 F eb 2 00 4 Transformations of elliptic hypergeometric integrals (2004) (0)
Q A ] 4 D ec 2 00 1 BC n-symmetric polynomials (0)
The EKG Sequence: 10927 (2004) (0)
Ju l 2 00 6 PROPERTIES OF GENERALIZED UNIVARIATE HYPERGEOMETRIC FUNCTIONS (2006) (0)
Difference Operators of Sklyanin and van Diejen Type (2013) (0)
The Main Theorems (2006) (0)
Classical Self-Dual Codes (2006) (0)
BUNDLES ON GENUS 2 CURVES AND TRIVECTORS (0)
Deformations of permutation representations of Coxeter groups (2012) (0)
Uniqueness of Polarization for the Autonomous 4-dimensional Painlevé-type Systems (2019) (0)
Maximal Isotropic Codes and Lattices (2006) (0)
Q A ] 2 0 A pr 2 00 5 Transformations of elliptic hypergeometric integrals (2008) (0)
Q A ] 1 M ar 2 00 3 BC n-symmetric polynomials (0)
The Category Quad (2006) (0)
Problems: 10550-10556 (1996) (0)
Functions of Several Complex Variables 32Xxx (2010) (0)
Further Examples of Self-Dual Codes (2006) (0)
J un 2 00 6 Correlation Functions for Random Involutions (2008) (0)
Enumeration of Self-Dual Codes (2006) (0)
Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant (2019) (0)
Filtered deformations of elliptic algebras (2021) (0)
S I ] 2 1 D ec 2 01 6 A symmetric difference-differential Lax pair for Painlevé VI (2016) (0)
Algebra & Number Theory (2014) (0)
Rationals to and Only to Rationals: 10555 (1998) (0)
M ay 2 00 2 The Lattice of N-Run Orthogonal Arrays (0)
Semiclassical biorthogonal functions, elliptic Painlevé, and discrete isomonodromy deformations (2012) (0)
C O ] 2 8 M ay 2 00 2 On Asymmetric Coverings and Covering Numbers (2013) (0)
0 A ug 2 00 0 Images of eigenvalue distributions under power maps (1999) (0)
On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums (2016) (0)
Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21-25, 2008, MPIM, Bonn, Germany) (2009) (0)
On squares, cubes, ... in Z[[x]]* (2005) (0)
Affine Macdonald conjectures and special values of Felder–Varchenko functions (2017) (0)
VANISHING INTEGRALS OF MACDONALD AND (2007) (0)
C A ] 2 J ul 2 00 8 An isomonodromy interpretation of the elliptic Painlevé equation . (2008) (0)
Q A ] 7 F eb 2 00 4 BC n-symmetric polynomials (2013) (0)
Ju n 20 00 Correlation functions for symmetrized increasing subsequences (2000) (0)
On the Existence of Similar SublatticesJ (1999) (0)
An Elliptic Garnier System (2017) (0)
A ] 1 6 Se p 20 03 Transformations of elliptic hypergeometric integrals (2003) (0)
Colored Designs and Z Codes (2005) (0)
A Nekrasov–Okounkov formula for Macdonald polynomials (2017) (0)
On the involutions fixing the class of a lattice (2003) (0)
Extremal and Optimal Codes (2006) (0)
The Type of a Self-Dual Code (2006) (0)
Weight Enumerators and Important Types (2006) (0)
A pr 2 00 1 The asymptotics of monotone subsequences of involutions (2008) (0)
Quotients of abelian varieties by reflection groups (2023) (0)
A pr 2 00 5 Recurrences for elliptic hypergeometric integrals (2008) (0)
A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals (2011) (0)

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