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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.
List of contents
Preface.- Benkart, G. and Halverson, T.: Partition Algebras and the Invariant Theory of the Symmetric Group.- Chen, L. and Tymoczko, J.: Affine Grassmannians and Hessenberg Schubert Cells.- Fishel, S.: A Survey of the Shi Arrangement.- Gillespie, M.: Variations on a Theme of Schubert Calculus.- Hicks, A.: Combinatorics of the Diagonal Harmonics.- Liu, F.: On Positivity of Ehrhart Polynomials.- Mason, S. K.: Recent Trends in Quasisymmetric Functions.- Mishna, M. J.: On Standard Young Tableaux of Bounded Height.- Novik, I.: A Tale of Centrally Symmetric Polytopes and Spheres.- Puskas, A.: Crystal Constructions in Number Theory.
About the author
Summary
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.
Report
"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)
