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- Eric M. Rains

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
44
Citations
12,071
147
World Ranking
1063
National Ranking
500

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.

- 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.

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

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.

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

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

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.

- 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)

- 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.

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)**

2141 Citations

Quantum nonlocality without entanglement

Charles H. Bennett;David P. DiVincenzo;Christopher A. Fuchs;Tal Mor.

Physical Review A **(1999)**

1210 Citations

Quantum Error Correction and Orthogonal Geometry

A. R. Calderbank;E. M. Rains;P. W. Shor;N. J. A. Sloane.

Physical Review Letters **(1997)**

898 Citations

Nonbinary quantum codes

E.M. Rains.

IEEE Transactions on Information Theory **(1999)**

450 Citations

Self-Dual Codes

E. M. Rains;N. J. A. Sloane.

arXiv: Combinatorics **(2002)**

435 Citations

A semidefinite program for distillable entanglement

E.M. Rains.

IEEE Transactions on Information Theory **(2001)**

380 Citations

Shadow bounds for self-dual codes

E.M. Rains.

IEEE Transactions on Information Theory **(1998)**

357 Citations

Transformations of elliptic hypergeometric integrals

Eric M. Rains.

Annals of Mathematics **(2010)**

354 Citations

Bound on distillable entanglement

E. M. Rains.

Physical Review A **(1999)**

343 Citations

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

Alexei Borodin;Eric M. Rains.

Journal of Statistical Physics **(2005)**

340 Citations

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