Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions
Abstract
Set partitions avoiding -crossing and -nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger's algorithm, Lin confirmed a conjecture due independently to the author and Martinez-Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-nonnesting partitions have the same cardinality. In this paper, we provide a bijective proof of this conjecture. Our bijection also enables us to provide a new bijective proof of a conjecture posed by Duncan and Steingr\'{\i}msson, which was proved by the author via an intermediate structure of growth diagrams for -fillings of Ferrers shapes.
Cite
@article{arxiv.1707.02408,
title = {Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions},
author = {Sherry H. F. Yan},
journal= {arXiv preprint arXiv:1707.02408},
year = {2017}
}