Štetje dreves : delo diplomskega seminarja

Podlogar, Petra (author), Konvalinka, Matjaž (mentor)

Drevesa so eno od klasičnih področij kombinatorike, teorije grafov in teoretičnega računalništva. Z različnimi kombinacijami lastnosti dobimo vrsto različnih tipov dreves, kot so dvojiška drevesa, Catalanova drevesa, ipd. Za nekatere družine dobimo tudi natančne preštevalne formule, za druge izpeljemo rodovne funkcije in/ali si ogledamo njihovo asimptotiko.

• Language: Slovenian
• Keywords: drevo, rodovna funkcija, Lagrangeeva inverzija, kombinatorika
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-120589
• UDC: 519.17
• COBISS.SI-ID: 58381059
• Publication date in RUL: 23.09.2020

Secondary language

• Language: English
• Title: Enumeration of trees

Abstract

Trees are one of the classical fields of combinatorics, graph theory and theoretical computer science. With different combinations of properties we get a series of different types of trees, such as binary trees, Catalan trees, etc. For some families we also get explicit formulas, for others we derive their generating functions and/or look at their asymptotic behavior.

• Keywords: tree, generating function, Lagrange inversion formula, combinatorics