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- W4300367613 abstract "We recall the occupancy problem introduced by Konheim & Weiss in 1966 and we consider parking functions as hash maps. Each car $c_i$ prefers parking space $p_i$ (the hash map $c_i mapsto p_i$ with $c_i$ is a key and $p_i$ an index into an array), if $p_i$ is occupied then $c_i$ the next available parking space (the hash table implementation using an open addressing strategy). This paper considers some others hash table implementations like hash tables with linked lists (with parking functions as hash maps). Using the Species Theory, we enumerate by Lagrange inversion those hash tables structures via a bijection with tree-like structures. This bijection provides a generalization of the Foata-Riordan bijection between parking functions and (forests of) rooted trees. Finally we show the number of hash tables with linked lists on a set of keys of cardinality $n$ is $n!C_n$, so the number of labeled binary trees with $n$ nodes." @default.
- W4300367613 created "2022-10-03" @default.
- W4300367613 creator A5037065995 @default.
- W4300367613 date "2015-03-13" @default.
- W4300367613 modified "2023-09-27" @default.
- W4300367613 title "Bijection: Parking-like structures and Tree-like structures" @default.
- W4300367613 doi "https://doi.org/10.48550/arxiv.1503.04245" @default.
- W4300367613 hasPublicationYear "2015" @default.
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