Algebraic Combinatorics (MATH 561)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Kağan Kurşungöz kursungoz@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Interactive,Communicative
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CONTENT

Group representations, representations of the symmetric group, combinatorial algorithms, symmetric functions, ordinary partitions, Young tableaux, plane partitions and applications in other enumerative problems.

OBJECTIVE

To provide a gentle introduction to algebraic combinatorics.

To acquaint the students with the sine-qua-non of combinatorial algorithms Robinson-Schensted-Knuth correspondence, basics of group representations, and the representations of the symmetric group.

LEARNING OUTCOME

Learn the definition of tableaux, semi-standard and standard (Young) Tableaux.
Be able to apply inserting-sliding operations
Learn the monoid pf words, and the interplay with tableaux via the Robinson-Schensted-Knuth correspondence
Learn the Littlewood-Richardson rule.
Learn the basics of group representations
Learn the representations of the symmetric group
Learn other basic combinatorial algorithms in the context of representations of the symmetric group and Young tableaux besides jeu-de-taquin, such as Viennot's construction.
Learn the basics of symmetric functions.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 25
Midterm 25
Assignment 25
Presentation 25

RECOMENDED or REQUIRED READINGS

Textbook

W. Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, Cambridge University Press, 1997

B. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Springer Science & Business Media, 2013.