Algebraic combinatorics and coinvariant spaces. (2009)

• Record Type: Book
• Further Information: Note: François Bergeron.
• Authors: Bergeron, François
• Contents: Combinatorial Objects; Permutations; Monomials; Diagrams; Partial Orders on Vectors; Young Diagrams; Partitions; The Young Lattice; Compositions; Words; Some Tableau Combinatorics; Tableaux; Insertion in Words and Tableaux; Jeu de Taquin; The RSK Correspondence; Viennot’s Shadows; Charge and Cocharge; Invariant Theory; Polynomial Ring; Root Systems; Coxeter Groups; Invariant and Skew-Invariant Polynomials; Symmetric Polynomials and Functions; The Fundamental Theorem of Symmetric Functions; More Basic Identities; Plethystic Substitutions; Antisymmetric Polynomials; Schur and Quasisymmetric Functions; A Combinatorial Approach; Formulas Derived from Tableau Combinatorics; Dual Basis and Cauchy Kernel; Transition Matrices; Jacobi–Trudi Determinants; Proof of the Hook Length Formula; The Littlewood–Richardson Rule; Schur-Positivity; Poset Partitions; Quasisymmetric Functions; Multiplicative Structure Constants; r-Quasisymmetric Polynomials; Representation Theory; Basic Representation Theory; Characters; Special Representations; Action of Sn on Bijective Tableaux; Irreducible Representations of Sn; Frobenius Transform; Restriction from Sn to Sn−1; Polynomial Representations of GL (V); Schur–Weyl Duality; Species Theory; Species of Structures; Generating Series; The Calculus of Species; Vertebrates and Rooted Trees; Generic Lagrange Inversion; Tensorial Species; Polynomial Functors; Commutative Algebra; Ideals and Varieties; Gröbner Basis; Graded Algebras; The Cohen–Macaulay Property; Coinvariant Spaces; Coinvariant Spaces; Harmonic Polynomials; Regular Point Orbits; Symmetric Group Harmonics; Graded Frobenius Characteristic of the Sn-Coinvariant; Space; Generalization to Line Diagrams; Tensorial Square; Macdonald Functions; Macdonald’s Original Definition; Renormalization; Basic Formulas; q, t-Kostka; A Combinatorial Approach; Nabla Operator; Diagonal Coinvariant Spaces; Garsia–Haiman Representations; Generalization to Diagrams; Punctured Partition Diagrams; Intersections of Garsia–Haiman Modules; Diagonal Harmonics; Specialization of Parameters; Coinvariant-Like Spaces; Operator-Closed Spaces; Quasisymmetric Modulo Symmetric; Super-Coinvariant Space; More Open Questions; Formulary; Some q-Identities; Partitions and Tableaux; Symmetric and Antisymmetric Functions; Integral Form Macdonald Functions; Some Specific Values
• Publisher Details: Ottawa, Ontario Wellesley, Massachusetts : Canadian Mathematical Society = Société mathématique du Canada A K Peters, Ltd
• Publication Date: 2009
• Copyright Date: 2009
• Extent: 1 online resource (227 pages), illustrations (some color)
• Subjects: 511/.6; Combinatorial analysis; Algebraic spaces; Algebraic spaces; Combinatorial analysis; Algebraic spaces; Combinatorial analysis; Electronic books
• Languages: English
• ISBNs: 9781439865071; 1439865078
• Related ISBNs: 9781568813240
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.