Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901150 | Applied Mathematics and Computation | 2018 | 7 Pages |
Abstract
Set partitions avoiding k-crossing and k-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 SteingrÃmsson, which was proved by the author via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sherry H.F. Yan,