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PreprintCC BY 4.0arXiv

A parking function analog of the Schröder numbers

  • Lucy Martinez
  • Doron Zeilberger
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Abstract

Pattern avoidance is a central topic in the study of permutations. Parking functions provide a natural setting in which to ask analogous questions. In this paper, we study parking functions whose parking permutations avoid the patterns $1234$ and $2134$, obtaining an analog of the Schröder numbers for parking functions. To enumerate these objects, we develop an enumeration scheme that runs in polynomial time and adapt the prefix-based framework introduced by Zeilberger in 1998, and later improved by Vatter, by instead using ``suffixes.''

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Cite

BibTeXRIS
BibTeX
@misc{martinez2026parking,
  title = {{A parking function analog of the Schröder numbers}},
  author = {Lucy Martinez and Doron Zeilberger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28650},
  eprint = {2609.28650},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28650},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A parking function analog of the Schröder numbers
AU  - Lucy Martinez
AU  - Doron Zeilberger
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28650
UR  - https://arxiv.org/abs/2609.28650
AB  - Pattern avoidance is a central topic in the study of permutations. Parking functions provide a natural setting in which to ask analogous questions. In this paper, we study parking functions whose parking permutations avoid the patterns $1234$ and $2134$, obtaining an analog of the Schröder numbers for parking functions. To enumerate these objects, we develop an enumeration scheme that runs in polynomial time and adapt the prefix-based framework introduced by Zeilberger in 1998, and later improved by Vatter, by instead using ``suffixes.''
ER  -