What is he best known for?
The fields of study he is best known for:
- Combinatorics
- Algebra
- Discrete mathematics
His main research concerns Combinatorics, Discrete mathematics, Partially ordered set, Algebra and Hilbert series and Hilbert polynomial.
Richard P. Stanley integrates Combinatorics with Polyhedral combinatorics in his research.
In general Discrete mathematics study, his work on Conjecture, Polytope and Legendre's equation often relates to the realm of Homogeneous, thereby connecting several areas of interest.
His Partially ordered set research includes themes of Weyl group, Transfer, Algebraic variety, Algebraic geometry and Real number.
His study on Profinite group and Group theory is often connected to Generating function and Local cohomology as part of broader study in Algebra.
Richard P. Stanley has included themes like Differential graded algebra, Hilbert–Poincaré series, Semimodular lattice, Vertex and Betti number in his Hilbert series and Hilbert polynomial study.
His most cited work include:
- Enumerative Combinatorics: Volume 1 (1599 citations)
- Enumerative Combinatorics: Index (1192 citations)
- Combinatorics and commutative algebra (1107 citations)
What are the main themes of his work throughout his whole career to date?
The scientist’s investigation covers issues in Combinatorics, Discrete mathematics, Symmetric group, Partially ordered set and Conjecture.
His studies in Symmetric function, Partition, Polytope, Permutation and Integer are all subfields of Combinatorics research.
His studies in Discrete mathematics integrate themes in fields like Function and Parity of a permutation.
His Symmetric group study is concerned with the larger field of Pure mathematics.
His Partially ordered set research incorporates themes from Generalization and Hyperplane.
The various areas that he examines in his Enumerative combinatorics study include Extremal combinatorics and Algebra over a field.
He most often published in these fields:
- Combinatorics (78.37%)
- Discrete mathematics (35.46%)
- Symmetric group (15.25%)
What were the highlights of his more recent work (between 2010-2021)?
- Combinatorics (78.37%)
- Discrete mathematics (35.46%)
- Conjecture (11.35%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Combinatorics, Discrete mathematics, Conjecture, Partially ordered set and Smith normal form.
His Combinatorics study frequently involves adjacent topics like Matrix.
His Discrete mathematics research is multidisciplinary, relying on both Distributive lattice, Arithmetic, Integer sequence and Product.
His Conjecture research is multidisciplinary, incorporating elements of Unimodality, Characterization, Chordal graph and Vertex.
In his study, Bijection is strongly linked to Lattice, which falls under the umbrella field of Partially ordered set.
The concepts of his Smith normal form study are interwoven with issues in Symmetric function and Lattice.
Between 2010 and 2021, his most popular works were:
- Formulae for Askey-Wilson moments and enumeration of staircase tableaux (40 citations)
- Smith normal form in combinatorics (36 citations)
- The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions (29 citations)
In his most recent research, the most cited papers focused on:
- Combinatorics
- Algebra
- Discrete mathematics
Richard P. Stanley mainly focuses on Combinatorics, Discrete mathematics, Conjecture, Product and Matrix.
Much of his study explores Combinatorics relationship to Polynomial.
His work in Discrete mathematics addresses issues such as Type, which are connected to fields such as Unimodality, Open problem and Binomial coefficient.
His research integrates issues of Simple graph, Partition, Chordal graph and Vertex in his study of Conjecture.
His Product research also works with subjects such as
- Random permutation that intertwine with fields like Rencontres numbers, Mixing and Parity of a permutation,
- Separation together with Random permutation statistics and Golomb–Dickman constant.
In general Matrix, his work in Smith normal form is often linked to Smith form linking many areas of study.
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