H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 44 Citations 10,747 126 World Ranking 809 National Ranking 391

Research.com Recognitions

Awards & Achievements

2018 - Fellow of the American Mathematical Society For contributions to quantum information theory and coding theory, the theory of random matrices, the study of special functions, non-commutative geometry and number theory.

Overview

What is he best known for?

The fields of study he is best known for:

  • Algebra
  • Mathematical analysis
  • Combinatorics

Eric M. Rains mainly investigates Combinatorics, Discrete mathematics, Linear code, Pure mathematics and Invariant. He has included themes like Quantum information science, Quantum entanglement and Subsequence in his Combinatorics study. The Discrete mathematics study combines topics in areas such as Longest increasing subsequence, Fixed point, Classical group and Algebraic number.

His Linear code study combines topics from a wide range of disciplines, such as Invariant theory and Algebra. In the subject of general Pure mathematics, his work in Rational function and Hypergeometric distribution is often linked to Probability theory and Aztec diamond, thereby combining diverse domains of study. The various areas that he examines in his Quantum convolutional code study include Stabilizer code, Concatenated error correction code, Quantum capacity and Decoherence-free subspaces.

His most cited work include:

  • Quantum error correction via codes over GF(4) (1200 citations)
  • Quantum nonlocality without entanglement (698 citations)
  • Quantum Error Correction and Orthogonal Geometry (585 citations)

What are the main themes of his work throughout his whole career to date?

The scientist’s investigation covers issues in Pure mathematics, Combinatorics, Discrete mathematics, Algebra and Macdonald polynomials. His Pure mathematics research is multidisciplinary, incorporating elements of Eigenvalues and eigenvectors and Mathematical analysis. Eric M. Rains combines subjects such as Classical group and Matrix, Unitary matrix with his study of Eigenvalues and eigenvectors.

His study in Combinatorics is interdisciplinary in nature, drawing from both Type, Invariant and Group. His Discrete mathematics study combines topics in areas such as Invariant theory, Quantum, Linear programming and Quantum codes, Linear code. His Linear code research incorporates themes from Hamming code and Concatenated error correction code.

He most often published in these fields:

  • Pure mathematics (44.65%)
  • Combinatorics (32.56%)
  • Discrete mathematics (24.65%)

What were the highlights of his more recent work (between 2015-2021)?

  • Pure mathematics (44.65%)
  • Moduli space (7.44%)
  • Macdonald polynomials (9.77%)

In recent papers he was focusing on the following fields of study:

Eric M. Rains mostly deals with Pure mathematics, Moduli space, Macdonald polynomials, Type and Lax pair. His Macdonald polynomials research is under the purview of Combinatorics. His work deals with themes such as Higgs boson and Riemann surface, which intersect with Combinatorics.

His Type research incorporates elements of Hypergeometric function, Gravitational singularity, Quantization, Star product and Orthogonal polynomials. To a larger extent, he studies Discrete mathematics with the aim of understanding Natural transformation. His Discrete mathematics research is multidisciplinary, incorporating perspectives in Affine group, Quantum affine algebra and Affine Hecke algebra.

Between 2015 and 2021, his most popular works were:

  • Multivariate Quadratic Transformations and the Interpolation Kernel (21 citations)
  • Commutation Relations and Discrete Garnier Systems (14 citations)
  • ABELIAN VARIETIES ISOGENOUS TO A POWER OF AN ELLIPTIC CURVE (9 citations)

In his most recent research, the most cited papers focused on:

  • Algebra
  • Mathematical analysis
  • Pure mathematics

His primary areas of investigation include Pure mathematics, Lax pair, Moduli space, Macdonald polynomials and Affine transformation. His Pure mathematics study frequently intersects with other fields, such as Generalization. His studies in Lax pair integrate themes in fields like Symmetry, Linear system, Differential and Symmetric difference.

His Moduli space research includes elements of Combinatorics, Riemann surface, Space, Polynomial and Higgs boson. His biological study spans a wide range of topics, including Hypergeometric function, Type, Bounded function, Partial fraction decomposition and Symplectic geometry. His work in Affine transformation addresses subjects such as Interpolation, which are connected to disciplines such as Kernel.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Quantum error correction via codes over GF(4)

A.R. Calderbank;E.M. Rains;P.M. Shor;N.J.A. Sloane.
international symposium on information theory (1997)

1644 Citations

Quantum nonlocality without entanglement

Charles H. Bennett;David P. DiVincenzo;Christopher A. Fuchs;Tal Mor.
Physical Review A (1999)

1108 Citations

Quantum Error Correction and Orthogonal Geometry

A. R. Calderbank;E. M. Rains;P. W. Shor;N. J. A. Sloane.
Physical Review Letters (1997)

819 Citations

Self-Dual Codes

E. M. Rains;N. J. A. Sloane.
arXiv: Combinatorics (2002)

435 Citations

Nonbinary quantum codes

E.M. Rains.
IEEE Transactions on Information Theory (1999)

408 Citations

Transformations of elliptic hypergeometric integrals

Eric M. Rains.
Annals of Mathematics (2010)

340 Citations

Shadow bounds for self-dual codes

E.M. Rains.
IEEE Transactions on Information Theory (1998)

337 Citations

A semidefinite program for distillable entanglement

E.M. Rains.
IEEE Transactions on Information Theory (2001)

331 Citations

Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs

Alexei Borodin;Eric M. Rains.
Journal of Statistical Physics (2005)

316 Citations

Bound on distillable entanglement

E. M. Rains.
Physical Review A (1999)

309 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us

Top Scientists Citing Eric M. Rains

Peter J. Forrester

Peter J. Forrester

University of Melbourne

Publications: 82

Alexei Borodin

Alexei Borodin

MIT

Publications: 75

Shao-Ming Fei

Shao-Ming Fei

Capital Normal University

Publications: 73

Patrik L. Ferrari

Patrik L. Ferrari

University of Bonn

Publications: 47

Patrick Solé

Patrick Solé

Télécom ParisTech

Publications: 42

Mark M. Wilde

Mark M. Wilde

Louisiana State University

Publications: 33

Ivan Corwin

Ivan Corwin

Columbia University

Publications: 32

Vyacheslav P. Spiridonov

Vyacheslav P. Spiridonov

Joint Institute for Nuclear Research

Publications: 31

Aaron Gulliver

Aaron Gulliver

University of Victoria

Publications: 30

Jinho Baik

Jinho Baik

University of Michigan–Ann Arbor

Publications: 30

Masahito Hayashi

Masahito Hayashi

Southern University of Science and Technology

Publications: 29

Tomohiro Sasamoto

Tomohiro Sasamoto

Tokyo Institute of Technology

Publications: 28

San Ling

San Ling

Nanyang Technological University

Publications: 26

Andreas Winter

Andreas Winter

Autonomous University of Barcelona

Publications: 25

Daniel Gottesman

Daniel Gottesman

Perimeter Institute

Publications: 25

Something went wrong. Please try again later.