Algebraic Combinatorics and Coinvariant Spaces
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A01=Francois Bergeron
advanced combinatorics
Algebraic Geometry
Author_Francois Bergeron
Category=PBV
Cohomology Ring
combinatorial algebra research
Diagonal Action
Dominance Order
Dyck Path
Elementary Symmetric Functions
enumerative combinatorics
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
finite Coxeter groups
function
graduate mathematics textbook
hilbert
Hilbert Series
Homogeneous Subspace
Hook Length Formula
Invariant Polynomials
irreducible
Jacobian Determinant
Left Regular Representation
Littlewood Richardson Rule
Macdonald Functions
Monomial Order
Monomials Xa
permutation statistics
polynomial
Regular Representation
representation
representation theory applications
schur
Schur Functions
Schur Polynomials
Schur Weyl Duality
series
standard
Standard Tableau
symmetric
Symmetric Functions
Symmetric Group
Symmetric Polynomials
tableau
Trivial Representation
Product details
- ISBN 9780367385460
- Weight: 453g
- Dimensions: 152 x 229mm
- Publication Date: 23 Oct 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and some commutative algebra, the main material provides links between the study of coinvariant—or diagonally coinvariant—spaces and the study of Macdonald polynomials and related operators. This gives rise to a large number of combinatorial questions relating to objects counted by familiar numbers such as the factorials, Catalan numbers, and the number of Cayley trees or parking functions. The author offers ideas for extending the theory to other families of finite Coxeter groups, besides permutation groups.
Bergeron, Francois
