Simetrične funkcije : magistrsko delo

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

V tem delu obravnavamo nekaj osnovnih družin simetričnih funkcij. Pogledamo si njihove lastnosti, dokažemo, da tvorijo baze za algebro simetričnih funkcij, in poiščemo prehode med bazami. Največ časa posvetimo Schurovim funkcijam, v sklopu katerih se srečamo z RSK algoritmom. Zaključimo z evalvacijami in specializacijami simetričnih funkcij.

• Language: Slovenian
• Keywords: razčlenitev, simetrične funkcije, evalvacije, specializacije
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-174501
• UDC: 519.1
• COBISS.SI-ID: 251449091
• Publication date in RUL: 03.10.2025

Secondary language

• Language: English
• Title: Symmetric functions

Abstract

In this work, we study several fundamental families of symmetric functions. We explore their properties, prove they form bases of the algebra of symmetric functions, and examine the transitions between these bases. Particular emphasis is placed on Schur functions, in the context of which we encounter the RSK algorithm. We conclude with evaluations and specializations of symmetric functions.

• Keywords: partition, symmetric functions, evaluations, specializations