Partition into Heapable Sequences, Heap Tableaux and a Multiset Extension of Hammersley's Process
نویسندگان
چکیده
We investigate partitioning of integer sequences into heapable subsequences (previously defined and established by Mitzenmacher et al. [BHMZ11]). 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.
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