Bijektivno dokazovanje identitet o razčlenitvah

diplomsko delo

Aleks Stepančič (Author), Matjaž Konvalinka (Mentor)

Abstract

V nalogi bomo predstavili bijektivne rezultate, povezane z razčlenitvami. Najprej je predstavljena terminologija in teoretične osnove rodovnih funkcij in razčlenitev, ki so osnova za delo. Za razumevanje povezave med bijek- tivnim dokazom in rodovnimi funkcijami, bomo spoznali dekompozicije Yo- ungovih diagramov. Predstavili bomo klasične rezultate Eulerjevega petko- tniškega izreka, kot je rekurzivna zveza za število razčlenitev ter Franklinovo involucijo. V preostanku dela obravnavamo orodja, potrebna za pridobitev dveh direktnih bijekcij rekurzivne zveze. Prvo je rang razčlenitve, ki služi kot osnova za Dysonovo preslikavo, s katero pridobimo eksplicitno direktno bijekcijo. Drugo orodje je princip involucije, ki nam nudi iterativen postopek za pridobitev druge direktne bijekcije.

Keywords

odsotnost zaposlenih;zdravstveni absentizem;napovedovanje zdravstvenega absentizma;podatkovna analiza;obogatitve podatkov;analiza ključnih atributov;računalništvo;matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[A. Stepančič]
UDC:	004.85: 331.316.2(043.2)
COBISS:	208498947
Views:	63
Downloads:	15
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Bijectively proving integer partitions identities
Secondary abstract:	In this thesis, we will present bijective results related to integer partitions. Initially, the terminology and theoretical foundations of generating functions and partitions, necessary for understanding the work, are introduced. To understand the connection between bijective proof and generating functions, we will explore the decompositions of Young diagrams. We will present classic results from Euler’s pentagonal theorem, such as the recursive relationship for the number of partitions and Franklin’s involution. In the remainder of the work, we address tools required to obtain two direct bijections of the recursive relationship. The first is the rank of partitions, which serves as a basis for Dyson’s mapping, with which we obtain an explicit direct bijection. The second tool is the principle of involution, which provides us with an iterative process to acquire another direct bijection.
Secondary keywords:	absenteeism,;data analysis;data enrichment;machine learning; key attribute analysis;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;Bolniški dopust;Izostajanje od dela;Strojno učenje;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	1 spletni vir (1 datoteka PDF (42 str.))
ID:	25078357