## Maximal chains in fillings of moon polyominoes

- April 10, 2015
- 2:30 p.m.
- LeConte 312

## Abstract

A famous classical result of Schensted states that the length of the longest increasing subsequence in a permutation is equal to the length of the first row of the corresponding insertion tableau. More recently, Chen et al. gave a generalization of this result relating the length of the maximal crossing in a set partition and the rows of the corresponding vacillating tableau. As a consequence, they proved the equidistribution of the size of the maximal crossing and the maximal nesting in set partitions. The fact that permutations and set partitions can be viewed as rook placements on special type of boards spurred interest in the study of the distribution of maximal chain length in fillings of more general boards known as moon polyominoes. In particular, Rubey proved that this distribution depends on the columns of the moon polyomino but not their order. His proof was algebraic and he raised the question of finding the corresponding bijective proof. In this talk I will provide a solution to this problem by providing an explicit bijection.