What is he best known for?
The fields of study he is best known for:
- Combinatorics
- Algebra
- Geometry
The scientist’s investigation covers issues in Combinatorics, Discrete mathematics, Noncrossing partition, Conjecture and Simplicial complex.
His study on Betti number, Quotient and Oriented matroid is often connected to Context and Upper and lower bounds as part of broader study in Combinatorics.
Victor Reiner has researched Discrete mathematics in several fields, including Statistics and Multivariate statistics.
His studies in Noncrossing partition integrate themes in fields like Finite field, Lattice and Polygon.
The various areas that Victor Reiner examines in his Conjecture study include Affine transformation, Unit, Associahedron, Permutohedron and Narayana number.
When carried out as part of a general Simplicial complex research project, his work on Abstract simplicial complex and Simplicial homology is frequently linked to work in Simplicial approximation theorem and Karamata's inequality, therefore connecting diverse disciplines of study.
His most cited work include:
- Resolutions of Stanley-Reisner rings and Alexander duality (300 citations)
- Faces of Generalized Permutohedra (262 citations)
- Non-crossing partitions for classical reflection groups (249 citations)
What are the main themes of his work throughout his whole career to date?
Victor Reiner focuses on Combinatorics, Discrete mathematics, Pure mathematics, Coxeter group and Partially ordered set.
His Combinatorics research focuses on Conjecture, Polytope, Matroid, Coxeter element and Symmetric group.
His Matroid research incorporates themes from Tutte polynomial and Simplicial complex.
Finite field and Graph are the subjects of his Discrete mathematics studies.
Pure mathematics is closely attributed to Algebra in his research.
His biological study spans a wide range of topics, including Type, Cartesian product and Lattice.
He most often published in these fields:
- Combinatorics (78.68%)
- Discrete mathematics (24.37%)
- Pure mathematics (18.27%)
What were the highlights of his more recent work (between 2014-2021)?
- Combinatorics (78.68%)
- Pure mathematics (18.27%)
- Coxeter element (7.61%)
In recent papers he was focusing on the following fields of study:
Victor Reiner mainly focuses on Combinatorics, Pure mathematics, Coxeter element, Reflection group and Partially ordered set.
His research links Hopf algebra with Combinatorics.
He combines subjects such as Critical group, Modulo, Regular representation and Finite group with his study of Pure mathematics.
His work deals with themes such as Coxeter complex, Hyperplane and Conjugacy class, which intersect with Coxeter element.
In his work, Permutation, Disjoint union and Symmetric group is strongly intertwined with Type, which is a subfield of Partially ordered set.
He interconnects Lattice and Cartesian product in the investigation of issues within Coxeter group.
Between 2014 and 2021, his most popular works were:
- Representation stability for cohomology of configuration spaces in $\mathbf{R}^d$ (24 citations)
- Poset edge densities, nearly reduced words, and barely set-valued tableaux (18 citations)
- Absolute order in general linear groups (14 citations)
In his most recent research, the most cited papers focused on:
- Combinatorics
- Algebra
- Geometry
Victor Reiner spends much of his time researching Combinatorics, Pure mathematics, Coxeter group, Partially ordered set and Coxeter element.
His Combinatorics study incorporates themes from Interpretation and Descent.
In the subject of general Pure mathematics, his work in Weyl group is often linked to Reflection group, Root of unity, Representation and Stability, thereby combining diverse domains of study.
His Partially ordered set research incorporates elements of Bruhat order, Lattice and Cartesian product.
His Coxeter element research is multidisciplinary, incorporating elements of Conjugacy class, Toric variety, Hyperplane, Morphism and Equivalence relation.
His study in Conjugacy class is interdisciplinary in nature, drawing from both Multiset, Graph, Lemma and Matroid.
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