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PreprintarXiv licencearXiv

Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind

  • Zuo-Ru Zhang
  • Hongkuan Zhao
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Abstract

We construct a bijection between $2143$-avoiding and $3421$-avoiding permutations that preserves the descent top set and the ascent top set and reverses the left-to-right order of the peaks. This bijection allows us to establish a bijection between $1243$-avoiding and $3412$-avoiding permutations with the same properties. These results refine two cases of a conjecture posed by Burstein and prove a conjecture posed by Burstein and Jones.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026refined,
  title = {{Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind}},
  author = {Zuo-Ru Zhang and Hongkuan Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30975},
  eprint = {2610.30975},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30975},
}
RIS
TY  - UNPB
TI  - Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind
AU  - Zuo-Ru Zhang
AU  - Hongkuan Zhao
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.30975
UR  - https://arxiv.org/abs/2610.30975
AB  - We construct a bijection between $2143$-avoiding and $3421$-avoiding permutations that preserves the descent top set and the ascent top set and reverses the left-to-right order of the peaks. This bijection allows us to establish a bijection between $1243$-avoiding and $3412$-avoiding permutations with the same properties. These results refine two cases of a conjecture posed by Burstein and prove a conjecture posed by Burstein and Jones.
ER  -