**Speaker**: Xu Zhu (朱旭), Shanghai Jiao Tong University

**Date**: Tue, Dec 01, 2015

**Time**: 16:00 - 16:50

**Venue**: Middle Meeting Room

**Title**: The cycle descent statistics of permutations

**Abstract**:

For each positive integer $n$, the following sets of combinatorial objects have the same size: (i) The set of drawings of rooted plane trees with $n+1$ vertices; (ii) The set of Klazar trees with $n+1$ vertices; (iii) The set of perfect matchings on $[2n]$ in which no even number is matched to a larger odd number; (iv) The set of cycle-descent permutations on $[n]$.

In this talk, we discuss some mathematics around the above four sets. Especially, we try to demonstrate a bijection between (iii) and (iv).

This is joint work with J. Ma, S. Ma and Y. Yeh.