Get it on Google Play
New! Download Unionpedia on your Android™ device!
Faster access than browser!

Algebraic combinatorics

Index Algebraic combinatorics

Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. [1]

82 relations: Abstract algebra, Affine space, Alain Lascoux, Alfred Young, Algebraic graph theory, American Mathematical Society, Association scheme, Benz plane, Bernd Sturmfels, Binary relation, Cambridge University Press, Character theory, Coding theory, Combinatorial commutative algebra, Combinatorial design, Combinatorial optimization, Combinatorics, Commutative algebra, Complement graph, Complete graph, Doron Zeilberger, Enumerative combinatorics, Euclidean geometry, Ferdinand Georg Frobenius, Finite field, Finite geometry, Finite set, Galois geometry, General linear group, Geometry, Gian-Carlo Rota, Gilbert de Beauregard Robinson, Graduate Texts in Mathematics, Graph theory, Group (mathematics), Group action, Group representation, Group theory, Integer, Inversive geometry, Isomorphism, Journal of Algebraic Combinatorics, Laguerre plane, Lattice (order), Linear algebra, Linear independence, Marcel-Paul Schützenberger, Mathematician, Mathematics, Mathematics Subject Classification, ..., Matroid, Möbius plane, Melvin Hochster, Neighbourhood (graph theory), Network theory, Non-Desarguesian plane, Partially ordered set, Percy Alexander MacMahon, Pixel, Point (geometry), Polyhedral combinatorics, Polytope, Projective plane, Projective space, Regular graph, Representation theory, Representation theory of the symmetric group, Richard P. Stanley, Ring of symmetric functions, Schubert calculus, Strongly regular graph, Symmetric function, Symmetric group, Symmetric polynomial, Symmetry in mathematics, The Princeton Companion to Mathematics, Topology, Turán graph, University of Cambridge, Vector space, W. V. D. Hodge, Young tableau. Expand index (32 more) »

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

New!!: Algebraic combinatorics and Abstract algebra · See more »

Affine space

In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

New!!: Algebraic combinatorics and Affine space · See more »

Alain Lascoux

Alain Lascoux (October 17, 1944 – October 20, 2013) was a French mathematician at the University of Marne la Vallée and Nankai University.

New!!: Algebraic combinatorics and Alain Lascoux · See more »

Alfred Young

Alfred Young, FRS (16 April 1873 – 15 December 1940) was a British mathematician.

New!!: Algebraic combinatorics and Alfred Young · See more »

Algebraic graph theory

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs.

New!!: Algebraic combinatorics and Algebraic graph theory · See more »

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

New!!: Algebraic combinatorics and American Mathematical Society · See more »

Association scheme

The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance.

New!!: Algebraic combinatorics and Association scheme · See more »

Benz plane

In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz.

New!!: Algebraic combinatorics and Benz plane · See more »

Bernd Sturmfels

Bernd Sturmfels (born March 28, 1962 in Kassel, West Germany) is a Professor of Mathematics and Computer Science at the University of California, Berkeley and is a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 2017.

New!!: Algebraic combinatorics and Bernd Sturmfels · See more »

Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

New!!: Algebraic combinatorics and Binary relation · See more »

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

New!!: Algebraic combinatorics and Cambridge University Press · See more »

Character theory

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix.

New!!: Algebraic combinatorics and Character theory · See more »

Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications.

New!!: Algebraic combinatorics and Coding theory · See more »

Combinatorial commutative algebra

Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline.

New!!: Algebraic combinatorics and Combinatorial commutative algebra · See more »

Combinatorial design

Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.

New!!: Algebraic combinatorics and Combinatorial design · See more »

Combinatorial optimization

In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.

New!!: Algebraic combinatorics and Combinatorial optimization · See more »


Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

New!!: Algebraic combinatorics and Combinatorics · See more »

Commutative algebra

Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.

New!!: Algebraic combinatorics and Commutative algebra · See more »

Complement graph

In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.

New!!: Algebraic combinatorics and Complement graph · See more »

Complete graph

No description.

New!!: Algebraic combinatorics and Complete graph · See more »

Doron Zeilberger

Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics.

New!!: Algebraic combinatorics and Doron Zeilberger · See more »

Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.

New!!: Algebraic combinatorics and Enumerative combinatorics · See more »

Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

New!!: Algebraic combinatorics and Euclidean geometry · See more »

Ferdinand Georg Frobenius

Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory.

New!!: Algebraic combinatorics and Ferdinand Georg Frobenius · See more »

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

New!!: Algebraic combinatorics and Finite field · See more »

Finite geometry

A finite geometry is any geometric system that has only a finite number of points.

New!!: Algebraic combinatorics and Finite geometry · See more »

Finite set

In mathematics, a finite set is a set that has a finite number of elements.

New!!: Algebraic combinatorics and Finite set · See more »

Galois geometry

Galois geometry (so named after the 19th century French Mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field).

New!!: Algebraic combinatorics and Galois geometry · See more »

General linear group

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.

New!!: Algebraic combinatorics and General linear group · See more »


Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

New!!: Algebraic combinatorics and Geometry · See more »

Gian-Carlo Rota

Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-born American mathematician and philosopher.

New!!: Algebraic combinatorics and Gian-Carlo Rota · See more »

Gilbert de Beauregard Robinson

Gilbert de Beauregard Robinson (1906–1992) was a Canadian mathematician most famous for his work on combinatorics and representation theory of the symmetric groups, including the Robinson-Schensted algorithm.

New!!: Algebraic combinatorics and Gilbert de Beauregard Robinson · See more »

Graduate Texts in Mathematics

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.

New!!: Algebraic combinatorics and Graduate Texts in Mathematics · See more »

Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

New!!: Algebraic combinatorics and Graph theory · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

New!!: Algebraic combinatorics and Group (mathematics) · See more »

Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

New!!: Algebraic combinatorics and Group action · See more »

Group representation

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

New!!: Algebraic combinatorics and Group representation · See more »

Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

New!!: Algebraic combinatorics and Group theory · See more »


An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

New!!: Algebraic combinatorics and Integer · See more »

Inversive geometry

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.

New!!: Algebraic combinatorics and Inversive geometry · See more »


In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

New!!: Algebraic combinatorics and Isomorphism · See more »

Journal of Algebraic Combinatorics

Journal of Algebraic Combinatorics is a peer-reviewed scientific journal covering algebraic combinatorics.

New!!: Algebraic combinatorics and Journal of Algebraic Combinatorics · See more »

Laguerre plane

In mathematics, a Laguerre plane is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane, named after the French mathematician Edmond Nicolas Laguerre.

New!!: Algebraic combinatorics and Laguerre plane · See more »

Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

New!!: Algebraic combinatorics and Lattice (order) · See more »

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

New!!: Algebraic combinatorics and Linear algebra · See more »

Linear independence

In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.

New!!: Algebraic combinatorics and Linear independence · See more »

Marcel-Paul Schützenberger

Marcel-Paul "Marco" Schützenberger (October 24, 1920 – July 29, 1996) was a French mathematician and Doctor of Medicine.

New!!: Algebraic combinatorics and Marcel-Paul Schützenberger · See more »


A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

New!!: Algebraic combinatorics and Mathematician · See more »


Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Algebraic combinatorics and Mathematics · See more »

Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH.

New!!: Algebraic combinatorics and Mathematics Subject Classification · See more »


In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces.

New!!: Algebraic combinatorics and Matroid · See more »

Möbius plane

In mathematics, a Möbius plane (named after August Ferdinand Möbius) is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane.

New!!: Algebraic combinatorics and Möbius plane · See more »

Melvin Hochster

Melvin Hochster (born August 2, 1943) is an eminent American mathematician, regarded as one of the leading commutative algebraists active today.

New!!: Algebraic combinatorics and Melvin Hochster · See more »

Neighbourhood (graph theory)

In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.

New!!: Algebraic combinatorics and Neighbourhood (graph theory) · See more »

Network theory

Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects.

New!!: Algebraic combinatorics and Network theory · See more »

Non-Desarguesian plane

In mathematics, a non-Desarguesian plane, named after Girard Desargues, is a projective plane that does not satisfy Desargues' theorem, or in other words a plane that is not a Desarguesian plane.

New!!: Algebraic combinatorics and Non-Desarguesian plane · See more »

Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

New!!: Algebraic combinatorics and Partially ordered set · See more »

Percy Alexander MacMahon

Percy Alexander MacMahon (born 26 September 1854, Sliema, British Malta – 25 December 1929, Bognor Regis, England) was a mathematician, especially noted in connection with the partitions of numbers and enumerative combinatorics.

New!!: Algebraic combinatorics and Percy Alexander MacMahon · See more »


In digital imaging, a pixel, pel, dots, or picture element is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen.

New!!: Algebraic combinatorics and Pixel · See more »

Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

New!!: Algebraic combinatorics and Point (geometry) · See more »

Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

New!!: Algebraic combinatorics and Polyhedral combinatorics · See more »


In elementary geometry, a polytope is a geometric object with "flat" sides.

New!!: Algebraic combinatorics and Polytope · See more »

Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

New!!: Algebraic combinatorics and Projective plane · See more »

Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

New!!: Algebraic combinatorics and Projective space · See more »

Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

New!!: Algebraic combinatorics and Regular graph · See more »

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

New!!: Algebraic combinatorics and Representation theory · See more »

Representation theory of the symmetric group

In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained.

New!!: Algebraic combinatorics and Representation theory of the symmetric group · See more »

Richard P. Stanley

Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.

New!!: Algebraic combinatorics and Richard P. Stanley · See more »

Ring of symmetric functions

In algebra and in particular in algebraic combinatorics, the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity.

New!!: Algebraic combinatorics and Ring of symmetric functions · See more »

Schubert calculus

In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry).

New!!: Algebraic combinatorics and Schubert calculus · See more »

Strongly regular graph

In graph theory, a strongly regular graph is defined as follows.

New!!: Algebraic combinatorics and Strongly regular graph · See more »

Symmetric function

In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.

New!!: Algebraic combinatorics and Symmetric function · See more »

Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

New!!: Algebraic combinatorics and Symmetric group · See more »

Symmetric polynomial

In mathematics, a symmetric polynomial is a polynomial in variables, such that if any of the variables are interchanged, one obtains the same polynomial.

New!!: Algebraic combinatorics and Symmetric polynomial · See more »

Symmetry in mathematics

Symmetry occurs not only in geometry, but also in other branches of mathematics.

New!!: Algebraic combinatorics and Symmetry in mathematics · See more »

The Princeton Companion to Mathematics

The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press.

New!!: Algebraic combinatorics and The Princeton Companion to Mathematics · See more »


In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

New!!: Algebraic combinatorics and Topology · See more »

Turán graph

No description.

New!!: Algebraic combinatorics and Turán graph · See more »

University of Cambridge

The University of Cambridge (informally Cambridge University)The corporate title of the university is The Chancellor, Masters, and Scholars of the University of Cambridge.

New!!: Algebraic combinatorics and University of Cambridge · See more »

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

New!!: Algebraic combinatorics and Vector space · See more »

W. V. D. Hodge

Sir William Vallance Douglas Hodge FRS FRSE (17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer.

New!!: Algebraic combinatorics and W. V. D. Hodge · See more »

Young tableau

In mathematics, a Young tableau (plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.

New!!: Algebraic combinatorics and Young tableau · See more »


[1] https://en.wikipedia.org/wiki/Algebraic_combinatorics

Hey! We are on Facebook now! »