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PreprintCC BY 4.0arXiv

On a conjecture concerning two-stack sortable permutations

  • Yongzhou Wen
  • Sherry H. F. Yan
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Abstract

The two-stack sortable permutations of length n are known to be equinumerous with permutations of length n avoiding the dashed patterns 3−1−4−2 and 2−41−3. In this paper, we confirm an intriguing conjecture posed by Claesson, Kitaev, and Steingrímsson, which asserts that the quadruple (comp,asc,ldr,rmax) is equidistributed on these two permutation classes. Here comp and asc count the number of components and ascents, respectively, ldr denotes the length of the initial decreasing run, and rmax denotes the number of right-to-left maxima. This is accomplished by constructing bijections between two-stack sortable permutations and β(1,0)-trees.

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Cite

BibTeXRIS
BibTeX
@misc{wen2026conjecture,
  title = {{On a conjecture concerning two-stack sortable permutations}},
  author = {Yongzhou Wen and Sherry H. F. Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29115},
  eprint = {2610.29115},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29115},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On a conjecture concerning two-stack sortable permutations
AU  - Yongzhou Wen
AU  - Sherry H. F. Yan
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29115
UR  - https://arxiv.org/abs/2610.29115
AB  - The two-stack sortable permutations of length n are known to be equinumerous with permutations of length n avoiding the dashed patterns 3−1−4−2 and 2−41−3. In this paper, we confirm an intriguing conjecture posed by Claesson, Kitaev, and Steingrímsson, which asserts that the quadruple (comp,asc,ldr,rmax) is equidistributed on these two permutation classes. Here comp and asc count the number of components and ascents, respectively, ldr denotes the length of the initial decreasing run, and rmax denotes the number of right-to-left maxima. This is accomplished by constructing bijections between two-stack sortable permutations and β(1,0)-trees.
ER  -