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Level: MSci
Title: Partitions and young tableaux
Supervisor:

Dr Matt Fayers
Research Area: Algebra
Description:

A partition is a just a weakly decreasing finite sequence of positive integers. A partition is often represented by its Young diagram, which is an array of boxes in the plane. When these boxes are filled with numbers, the resulting diagram is a Young tableau. These have inherent combinatorial interest, as well as applications to areas such as symmetric functions representation theory of the symmetric groups. A student doing this project would start with Fulton's book, and give an account of some of the ideas there, perhaps expanding from other references. Particular sub-topics that might be covered are the hook-length formula, and Littlewood–Richardson coefficients.
Further Reading:
  • W. Fulton, Young Tableaux. London Mathematical Society, 1997.
Key Modules:

None.
Other Information:
Current Availability: Yes