A new approach to Naples parking functions through complete parking preferences
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916243918815232 |
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| author | Ferrari, Luca Verciani, Francesco |
| author_facet | Ferrari, Luca Verciani, Francesco |
| contents | Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous spots, before proceeding forward as usual. In this work we introduce the notion of a complete parking preference, through which we are able to give some information on the combinatorics of Naples parking functions. Roughly speaking, a complete parking preference is a parking preference such that, for any index $j$, there are more cars with preference at least $j$ than spots available from $j$ onward. We provide a characterization of Naples parking functions in terms of certain complete subsequences of them. As a consequence of this result we derive a characterization of permutation-invariant Naples parking functions which turns out to be equivalent to the one given by (Carvalho et al., 2021), but using a totally different approach (and language). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new approach to Naples parking functions through complete parking preferences Ferrari, Luca Verciani, Francesco Combinatorics 05A05, 05A99 Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous spots, before proceeding forward as usual. In this work we introduce the notion of a complete parking preference, through which we are able to give some information on the combinatorics of Naples parking functions. Roughly speaking, a complete parking preference is a parking preference such that, for any index $j$, there are more cars with preference at least $j$ than spots available from $j$ onward. We provide a characterization of Naples parking functions in terms of certain complete subsequences of them. As a consequence of this result we derive a characterization of permutation-invariant Naples parking functions which turns out to be equivalent to the one given by (Carvalho et al., 2021), but using a totally different approach (and language). |
| title | A new approach to Naples parking functions through complete parking preferences |
| topic | Combinatorics 05A05, 05A99 |
| url | https://arxiv.org/abs/2405.07522 |