##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Jeff Remmel

#### UCSD

## Ascent Sequences, 2+2-Free Posets, Upper Triangular Matrices, and Genocchi Numbers

##### Abstract:

The combinatorics of the Genocchi numbers was developed by Dumont and various co-authors in the 70's and 80's. More recently, Bousquet-Melou, Claesson, Dukes, Kitaev and Parviainen showed that the 2+2-free posets are in bijection with so-called ascent sequences and with non-negative integer valued upper triangular matrices which have no zero rows or columns. We will show how the Genocchi numbers can be interpreted as the number of up-down ascent sequences thus connecting these various classes of combinatorial objects.

### October 5, 2010

### 4:00 PM

### AP&M 7321

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