PreprintCC BY 4.0arXiv
Pattern avoidance classes of parking permutations with fixed lucky sets
Abstract
For a parking function, the resulting sequence after all cars have parked is called the associated parking permutation. For each parking function, cars that park in their preferred spot are called lucky cars. In this paper, we enumerate parking permutations that avoid a specified set of permutation patterns in S3 and whose lucky cars are the first k cars. Often, the enumeration simplifies to a product of a fraction with a binomial coefficient, recovering existing sequences in the OEIS. For two of the classes, the enumerations are new sequences.
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BibTeX
@misc{ferreri2026pattern,
title = {{Pattern avoidance classes of parking permutations with fixed lucky sets}},
author = {Melanie Ferreri and Lucy Martinez},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07267},
eprint = {2611.07267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07267},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pattern avoidance classes of parking permutations with fixed lucky sets
AU - Melanie Ferreri
AU - Lucy Martinez
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07267
UR - https://arxiv.org/abs/2611.07267
AB - For a parking function, the resulting sequence after all cars have parked is called the associated parking permutation. For each parking function, cars that park in their preferred spot are called lucky cars. In this paper, we enumerate parking permutations that avoid a specified set of permutation patterns in S_3 and whose lucky cars are the first k cars. Often, the enumeration simplifies to a product of a fraction with a binomial coefficient, recovering existing sequences in the OEIS. For two of the classes, the enumerations are new sequences.
ER -