GAUSS Series

Upcoming Seminars for Spring Semester

Unless otherwise noted, the Spring Semester Seminars will be held on Fridays from 3:00pm - 3:50pm in PB 390.

March 28, 2014; 3:30PM in PB 390: Elaina Aceves and Jennifer Elder (Fresno State Students)

Title:  Young Tableaux

Abstract: Young tableaux are combinatorial objects introduced by Alfred Young in 1900, and have numerous applications, not only in combinatorics but also in other areas in mathematics. In particular, Young tableaux are intimately related to the symmetric and general linear groups.

A Young diagram of a partition n = a+b+...+c, for a list a, b,..., c of k positive integers with a ≥ b ≥ … ≥ c is an arrangement of n square boxes in k rows, such that the boxes are left-justified, the first row is of length a, the second row of length b, and so on, with the k-th row of length c. A Young tableau of a Young diagram is obtained by placing the numbers 1,...,n in the n boxes of the diagram.

The partitions of integers less than or equal to mn in which there are at most n parts and in which no part is larger than m correspond to Young tableaux which fit inside an m×n rectangle, and to lattice paths which travel from the upper right corner of the rectangle to the lower left corner in m+n leftward and downward steps. What is the number of Young diagrams fitting inside an m×n rectangle?


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