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 1+ √5/2 ・ ln(n). Finally we give a heap-based extension of Young tableaux, prove a hook inequality and an extension of the Robinson-Schensted correspondence.
CITATION STYLE
Istrate, G., & Bonchiş, C. (2015). Partition into heapable sequences, heap tableaux and a multiset extension of Hammersley’s process. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9133, pp. 261–271). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_22
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