ENGLISH

Recent Trends in Algebraic Combinatorics

By Helene Barcelo , Gizem Karaali , Rosa Orellana

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-05140-2, 978-3-030-05141-9
Language
english
Format
PDF
Filesize
6 MB (6685665 bytes)
Series
Association for Women in Mathematics Series 16
Edition
1st ed.
Pages
VII, 362\364
Time added
2019-04-19 19:00:00
Mathematics; Combinatorics; Algebra

Description

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. Front Matter ....Pages i-vii Partition Algebras and the Invariant Theory of the Symmetric Group (Georgia Benkart, Tom Halverson)....Pages 1-41 Affine Grassmannians and Hessenberg Schubert Cells (Linda Chen, Julianna Tymoczko)....Pages 43-74 A Survey of the Shi Arrangement (Susanna Fishel)....Pages 75-113 Variations on a Theme of Schubert Calculus (Maria Gillespie)....Pages 115-158 Combinatorics of the Diagonal Harmonics (Angela Hicks)....Pages 159-188 On Positivity of Ehrhart Polynomials (Fu Liu)....Pages 189-237 Recent Trends in Quasisymmetric Functions (Sarah K. Mason)....Pages 239-279 On Standard Young Tableaux of Bounded Height (M. J. Mishna)....Pages 281-303 A Tale of Centrally Symmetric Polytopes and Spheres (Isabella Novik)....Pages 305-331 Crystal Constructions in Number Theory (Anna Puskás)....Pages 333-362

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