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Partition into Heapable Sequences, Heap Tableaux and a Multiset Extension of Hammersley’s Process

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Combinatorial Pattern Matching (CPM 2015)

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Abstract

We investigate partitioning of integer sequences into heapable subsequences (previously defined and established by Byers et al.). We show that an extension of patience sorting computes the decomposition into a minimal number of heapable subsequences (MHS). We connect this parameter to an interactive particle system, a multiset extension of Hammersley’s process, and investigate its expected value on a random permutation. In contrast with the (well studied) case of the longest increasing subsequence, we bring experimental evidence that the correct asymptotic scaling is \(\frac{1+\sqrt{5}}{2}\cdot \ln (n)\). Finally we give a heap-based extension of Young tableaux, prove a hook inequality and an extension of the Robinson-Schensted correspondence.

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Acknowledgment

This research has been supported by CNCS IDEI Grant PN-II-ID-PCE-2011-3-0981 “Structure and computational difficulty in combinatorial optimization: an interdisciplinary approach”.

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Authors and Affiliations

  1. Department of Computer Science, West University of Timişoara, Timişoara, Romania

    Gabriel Istrate & Cosmin Bonchiş

  2. e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, 300223, Timişoara, Romania

    Gabriel Istrate & Cosmin Bonchiş

Authors
  1. Gabriel Istrate
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  2. Cosmin Bonchiş
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Corresponding author

Correspondence to Gabriel Istrate .

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Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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Istrate, G., Bonchiş, C. (2015). Partition into Heapable Sequences, Heap Tableaux and a Multiset Extension of Hammersley’s Process. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

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