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Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions

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  • Yan, Sherry H.F.

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.

Suggested Citation

  • Yan, Sherry H.F., 2018. "Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 24-30.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:24-30
    DOI: 10.1016/j.amc.2017.12.021
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