##### Department of Mathematics,

University of California San Diego

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### Math 196 - Student Colloquium

## Joshua Swanson

#### UC San Diego

## Asymptotics of Mahonian statistics

##### Abstract:

Percy MacMahon introduced the ``major index'' of a permutation a century ago and proved that it has the same distribution as the ``inversion number''. Such statistics are now called ``Mahonian''. Baxter and Zeilberger considered the joint distribution of inversions and the major index on permutations and showed they are jointly independently asymptotically normally distributed. However, Baxter-Zeilberger's argument has no hope of giving a more precise ``local limit theorem'' and Zeilberger subsequently offered a \$300 reward for a different proof. This is the story of that reward.

### October 16, 2020

### 3:00 PM

### Contact Glenn Tesler for Zoom link

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