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

Conference paper

DOI: 10.1007/978-3-319-19929-0_22

Volume 9133 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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.

Keywords

Heapable sequences Hammersley process Heap tableaux 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceWest University of TimişoaraTimişoaraRomania
  2. 2.e-Austria Research InstituteTimişoaraRomania