Dokazi formule o kljukah : magistrsko delo

Jerman, Lara (author), Konvalinka, Matjaž (mentor)

V delu predstavimo problem števila standardnih Youngovih tabel ter formulo o kljukah, ki podaja odgovor. Obravnavamo tudi poševne tabele. Zberemo in povzamemo zgodovino različnih dokazov te formule ter pregledamo skice posameznih dokazov. Podrobno predstavimo štiri dokaze: 1) Frame, Robinson in Thrall (izvirni); 2) Greene, Nijenhuis in Wilf (verjetnostni); 3) Novelli, Pak in Stoyanovskii (z bijekcijo); 4) Konvalinka (z bijekcijo).

• Language: Slovenian
• Keywords: formula o kljukah, dokazi, preštevalna kombinatorika
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics; FRI - Faculty of Computer and Information Science
• Year: 2020
• PID: 20.500.12556/RUL-121270
• COBISS.SI-ID: 33064195
• Publication date in RUL: 02.10.2020

Secondary language

• Language: English
• Title: Proofs of hook-length formula

Abstract

In this thesis we present the problem of the number of standard Young tableux and the hook-length formula, which supplies the result. We also touch on skew-shape tableux. We collect and summarize the history of proofs of this formula and review sketches of individual proofs. We present four proofs in detail: 1) Frame, Robinson and Thrall (original); 2) Greene, Nijenhuis and Wilf (probabilistic); 3)Novelli, Pak and Stoyanovskii (bijective); 4) Konvalinka (bijective).

• Keywords: hook-length formula, proofs, enumerative combinatorics