Recent Trends in Algebraic Combinatorics

1. Front Matter

   Pages i-vii

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2. Partition Algebras and the Invariant Theory of the Symmetric Group

   • Georgia Benkart, Tom Halverson

   Pages 1-41

3. Affine Grassmannians and Hessenberg Schubert Cells

   • Linda Chen, Julianna Tymoczko

   Pages 43-74

4. A Survey of the Shi Arrangement

   • Susanna Fishel

   Pages 75-113

5. Variations on a Theme of Schubert Calculus

   • Maria Gillespie

   Pages 115-158

6. Combinatorics of the Diagonal Harmonics

   • Angela Hicks

   Pages 159-188

7. On Positivity of Ehrhart Polynomials

   • Fu Liu

   Pages 189-237

8. Recent Trends in Quasisymmetric Functions

   • Sarah K. Mason

   Pages 239-279

9. On Standard Young Tableaux of Bounded Height

   • M. J. Mishna

   Pages 281-303

10. A Tale of Centrally Symmetric Polytopes and Spheres

    • Isabella Novik

    Pages 305-331

11. Crystal Constructions in Number Theory

    • Anna Puskás

    Pages 333-362

This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools.

Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.

• Algebraic Combinatorics
• Algebra
• Group Theory
• Representation Theory
• Number Theory
• Survey papers on algebraic combinatorics
• Partition Algebras
• symmetric polytopes and spheres
• Shi Arrangement
• diagonal harmonics
• Schubert Calculus
• Ehrhart Polynomials
• women in algebraic combinatorics
• Association for Women in Mathematics
• recent trends in algebraic combinatorics
• combinatorics

"This is a collection of nine independent research papers. … the main use of the book will be as reference material. The individual chapters will be useful tools for researchers working in relevant fields.” (Miklós Bón, MAA Reviews, June 03, 2019)

• Mathematical Sciences Research Institute , Berkeley, USA

  Hélène Barcelo

• Department of Mathematics, Pomona College, Claremont, USA

  Gizem Karaali

• Department of Mathematics, Dartmouth College, Hanover, USA

  Rosa Orellana

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