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Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions.
- Source :
-
Applied Mathematics & Computation . May2018, Vol. 325, p24-30. 7p. - Publication Year :
- 2018
-
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 Steingrímsson, which was proved by the author via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIJECTIONS
*ALGORITHMS
*KERNEL functions
*COMBINATORICS
*MATHEMATICAL sequences
Subjects
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 325
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 127791973
- Full Text :
- https://doi.org/10.1016/j.amc.2017.12.021