Almost-sure asymptotic for the number of heaps inside a random sequence

@article{Basdevant2017AlmostsureAF,
  title={Almost-sure asymptotic for the number of heaps inside a random sequence},
  author={Anne-Laure Basdevant and Arvind Singh},
  journal={arXiv: Probability},
  year={2017}
}
We study the minimum number of heaps required to sort a random sequence using a generalization of Istrate and Bonchis's algorithm (2015). In a previous paper, the authors proved that the expected number of heaps grows logarithmically. In this note, we improve on the previous result by establishing the almost-sure and L 1 convergence. 
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