Recent trends in algebraic combinatorics. (2019)

• Record Type: Book
• Further Information: Note: Hélène Barcelo, Gizem Karaali, Rosa Orellana, editors.
• Editors: Barcelo, Hélène, 1954-; Karaali, Gizem, 1974-; Orellana, Rosa
• Contents: Intro; Preface; Contents; Partition Algebras and the Invariant Theory of the Symmetric Group; 1 Introduction; 2 Restriction-Induction Bratteli Diagrams and Vacillating Tableaux; 2.1 Generalities on Restriction and Induction; 2.2 The Restriction-Induction Bratteli Diagram; 2.3 Restriction and Induction for the Symmetric Group Pair (Sn, Sn-1); 3 Set Partitions; 3.1 Multiplicities from a Permutation Module Perspective; 3.2 Set-Partition Tableaux; 3.3 Bijections; 4 The Partition Algebra ¶k(n); 4.1 The Diagram Basis of the Partition Algebra ¶k(n); 4.2 The Orbit Basis; 4.3 Change of Basis 2.3 Decomposition into Schubert Cells3 Affine Grassmannian Permutations; 3.1 Coset Description for the Affine Grassmannian; 3.2 Geometric Linear Model for the Affine Grassmannian; 3.3 Affine Grassmannian Permutations and Skyline Diagrams; 4 Affine Schubert Cells; 5 Descriptions of Affine Schubert Cells: Bit Sequence, Linear Model, Cores, and Partitions; 6 (Grassmannian) Hessenberg Schubert Cells and Varieties; 6.1 Hessenberg Varieties; 6.2 Hessenberg Schubert Cells and Varieties; 6.3 Grassmannian Hessenberg Schubert Cells 6.4 Hessenberg Schubert Varieties and Grassmannian Hessenberg Schubert Varieties6.5 Minimal Hessenberg Schubert Cells; 7 Affine Schubert Cells and Hessenberg Schubert Cells; References; A Survey of the Shi Arrangement; 1 Background; 1.1 Root Systems and Coxeter Group Notation; 1.2 A Taste of Coxeter Combinatorics, Type A; 1.3 Deformation of Coxeter Arrangements; 2 Origin; 2.1 Kazhdan-Lusztig Cells; 2.2 Shi Regions and Kahzdan-Lusztig Cells; 3 Enumeration; 3.1 The Number of Shi Regions, Part 1; 3.2 Interlude; 3.3 The Number of Shi Regions, Part 2; 3.4 The Number of Shi Regions, Part 3 3.5 The Number of Shi Regions, Part 43.6 More; 3.7 The Ish and the Shi; 3.8 Extended Shi Arrangement; 4 Connections; 4.1 Decompositions Numbers and the Shi Arrangement; 4.2 Finite Automata and Reduced Expressions; 4.3 More Connections; 5 Further Developments; 6 Themes We Haven't Included; References; Variations on a Theme of Schubert Calculus; 1 Introduction; 1.1 ``Variations on a Theme''; 2 Background on Projective Space; 2.1 Affine Patches and Projective Varieties; 2.2 Points, Lines, and m-Planes in Projective Space; 2.3 Problems; 3 Theme: The Grassmannian; 3.1 Projective Variety Structure
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource (vii, 362 pages), illustrations (some color)
• Subjects: 511/.6; Combinatorial analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030051419; 3030051412
• Related ISBNs: 9783030051402; 3030051404
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed January 31, 2019).
• 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.