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Parkirne funkcije
ID Laharnar, Anja (Author), ID Konvalinka, Matjaž (Mentor) More about this mentor... This link opens in a new window

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Abstract
Parkirne funkcije so prvič formulirali za prikaz delovanja zgoščenih funkcij. Od takrat naprej se raziskovalci srečujejo z njimi na mnogih različnih področjih, v njihovi osnovni obliki in posplošenih oblikah. V tem diplomskem delu predstavimo parkirne funkcije in njihove povezave z drugimi področji. Obravnavmo zvezo s Prüferjevo kodo in označenimi drevesi. Raziščemo bijekcije z mrežo nekrižajočih se razdelitev, dovoljenimi pari vhodov in izhodov prioritetne vrste ter Shijevo razporeditvijo. Opišemo grafični prikaz parkirnih funkcij s pomočjo označenih Dyckovih poti. Preštejemo število parkirnih funkcij z dano končno razporeditvijo. Predstavimo tudi u-parkirne funkcije, posplošitev, ki jih preštejemo s pomočjo parkirnega politopa.

Language:Slovenian
Keywords:kombinatorika, parkirna funkcija, Prüferjeva koda, \linebreak označeno drevo, nekrižajoča se razdelitev, prioritetna vrsta, Shijeva razporeditev, označena Dyckova pot, u-parkirna funkcija, parkirni politop
Work type:Bachelor thesis/paper
Typology:2.11 - Undergraduate Thesis
Organization:FRI - Faculty of Computer and Information Science
Year:2025
PID:20.500.12556/RUL-167936 This link opens in a new window
COBISS.SI-ID:232209155 This link opens in a new window
Publication date in RUL:20.03.2025
Views:585
Downloads:205
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Secondary language

Language:English
Title:Parking functions
Abstract:
Parking functions were introduced during the research of hash functions as a presentation of the way they function. Since then, researchers encounter them in various areas, in their base and generalized forms. In this thesis we present parking functions and their connections with other areas. We discuss their relationship with Prüfer code and labeled trees. We also explore bijections with lattice of noncrossing partitions, allowed input-output pairs in a priority queue and Shi arrangement. For a graphical presentation of parking functions, we describe them via labeled Dyck paths. We count parking functions with a given final arrangement. In the end, we present u-parking functions, that are a generalization, and count them with the help of the parking polytope.

Keywords:combinatorics, parking function, Prüfer code, labeled tree, noncrossing partition, priority queue, Shi arrangement, labeled Dyck path, u-parking function, parking polytope

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