##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Sami H Assaf

#### MIT

## Applications of Dual Equivalence

##### Abstract:

A dual equivalence for an arbitrary collection of combinatorial objects endowed with a descent set is a relation for which equivalence classes group together terms according to the Schur expansion of the corresponding generating function. After outlining the definition of dual equivalence, we'll present three main applications: the Schur expansion of Macdonald polynomials, Schur positivity of k-Schur functions (joint with S. Billey), and a combinatorial rule for the Littlewood-Richardson coefficients of the Grassmannian in the special case of a Schubert polynomial times a Schur function (joint with N. Bergeron and F. Sottile).

Hosts: Fan Chung Graham and Jeff Remmel

### January 18, 2011

### 3:00 PM

### AP&M 6402

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