search query: @keyword Simplex / total: 2
reference: 1 / 2
« previous | next »
Author:Loiskekoski, Lauri
Title:Resolutions and associated primes of powers of ideals
Ideaalien potenssien resoluutiot ja assosioidut alkuideaalit
Publication type:Master's thesis
Publication year:2014
Pages:v + 24      Language:   eng
Department/School:Matematiikan ja systeemianalyysin laitos
Main subject:Matematiikka   (Mat-1)
Supervisor:Engström, Alexander
Instructor:
Electronic version URL: http://urn.fi/URN:NBN:fi:aalto-201507013684
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
Instructions

Reading digital theses in the closed network of the Aalto University Harald Herlin Learning Centre

In the closed network of Learning Centre you can read digital and digitized theses not available in the open network.

The Learning Centre contact details and opening hours: https://learningcentre.aalto.fi/en/harald-herlin-learning-centre/

You can read theses on the Learning Centre customer computers, which are available on all floors.

Logging on to the customer computers

  • Aalto University staff members log on to the customer computer using the Aalto username and password.
  • Other customers log on using a shared username and password.

Opening a thesis

  • On the desktop of the customer computers, you will find an icon titled:

    Aalto Thesis Database

  • Click on the icon to search for and open the thesis you are looking for from Aaltodoc database. You can find the thesis file by clicking the link on the OEV or OEVS field.

Reading the thesis

  • You can either print the thesis or read it on the customer computer screen.
  • You cannot save the thesis file on a flash drive or email it.
  • You cannot copy text or images from the file.
  • You cannot edit the file.

Printing the thesis

  • You can print the thesis for your personal study or research use.
  • Aalto University students and staff members may print black-and-white prints on the PrintingPoint devices when using the computer with personal Aalto username and password. Color printing is possible using the printer u90203-psc3, which is located near the customer service. Color printing is subject to a charge to Aalto University students and staff members.
  • Other customers can use the printer u90203-psc3. All printing is subject to a charge to non-University members.
Location:P1 Ark Aalto  1120   | Archive
Keywords:commutative algebra
independent set
graph theory
independence structure
simplex
critical subgraph
chromatic number
kommutatiivinen algebra
verkkoteoria
itsenäinen joukko
soluresoluutio
kriittinen aliverkko
kromaattinen luku
Abstract (eng): Independent sets are subsets of a graph where none of the nodes have links between them.
Finding the largest independent subsets and covering a graph by independent subsets are problems commonly encountered in combinatorial optimization.

In this thesis we study the independent sets of a graph and more general independence systems with the tools of commutative algebra.
We build a poset from the independent sets of a graph and associate an ideal in a commutative ring to it.
We calculate the associated primes and the free resolution of this ideal and its powers.

We show that the free resolution can be found geometrically as a cell resolution by embedding the poset to a space with as many dimensions as the graph has vertices.
Similarly the associated primes can be found by looking for the critical subgraphs which are subgraphs of the graph whose chromatic number is reduced by one when any of the vertices of the graph is removed.
Abstract (fin): Itsenäiset joukot ovat verkkojen osajoukkoja, joissa solmujen välillä ei ole yhtään linkkiä.
Mahdollisimman suurten itsenäisten joukkojen löytäminen ja verkon peittäminen itsenäisillä joukoilla ovat kombinatorisessa optimoinnissa vastaan tulevia ongelmia.

Tässä työssä tutkitaan verkkojen itsenäisiä joukkoja ja yleisempiä itsenäisyysrakenteita kommutatiivisen algebran keinoin.
Rakennamme verkon itsenäisistä joukoista osittain järjestetyn joukon, johon liitämme kommutatiivisen renkaan ideaalin.
Laskemme tälle ideaalille ja sen potensseille assosioidut alkuideaalit sekä vapaan resoluution.

Osoitamme, että tämän ideaalin vapaan resoluution pystyy luomaan soluresoluutiona upottamalla osittain järjestetty joukko avaruuteen, jonka ulottuvuuksien määrä on sama kuin verkon solmujen määrä.
Vastaavasti assosioitu alkuideaali löytyy analysoimalla verkon kriittisiä aliverkkoja, eli verkkoja joiden kromaattinen luku laskee yhdellä, mikäli mikä tahansa verkon solmuista poistetaan.
ED:2014-06-16
INSSI record number: 49209
+ add basket
« previous | next »
INSSI