prikaz prve stranice dokumenta Kombinatorni problemi distribucija
  Download
PDF 413.97 KB
master's thesis
Kombinatorni problemi distribucija
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:224246
Polić, Barbara
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Polić, B. (2019). Kombinatorni problemi distribucija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:224246

Polić, Barbara. "Kombinatorni problemi distribucija." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:224246

Polić, Barbara. "Kombinatorni problemi distribucija." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:224246

Polić, B. (2019). 'Kombinatorni problemi distribucija', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:224246

Polić B. Kombinatorni problemi distribucija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:224246

B. Polić, "Kombinatorni problemi distribucija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:224246

Metadata
TitleKombinatorni problemi distribucija
AuthorBarbara Polić
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberOzren Perše (član povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-04-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu proučavaju se razne vrste distribucija koristeći model kuglica i kutija uz određene uvjete kao što je različitost kuglica, različitost kutija, ograničenost kutija itd. Za jednake kutije smo problem povezali s particijama skupa (pa time i sa Stirlingovim brojem druge vrste) u slučaju kada se kuglice razlikuju, odnosno s particijom prirodnog broja za jednake kuglice. U oba slučaja pripadni broj distribucija zadovoljava jednostavnu rekurzivnu formulu koju smo implementirali u programskom jeziku Python 3.4. Za različite kutije i različite kuglice smo koristili permutacije i kombinacije zajedno s nekim rezultatima dobivenim u slučajevima s jednakim kutijama i različitim kuglicama dok je problem s jednakim kuglicama bio složeniji te su bile potrebne FUI i FI formule. Dobivena je veza s brojem injekcija, surjekcija i funkcija a tako i formule za Stirlingov broj druge vrste i Bellov broj. Na kraju, dobiveni rezultati su bili tablično prikazani.
Abstract (english)
This thesis studies different distributions using the box-ball model with certain criteria such as inequal balls, inequal boxes, boxes with limit etc. For equal boxes we linked the problem to set partitions (Stirling number of the second kind) when the balls are inequal and respectively with partition of a natural number when the balls are equal. In both cases the number of distributions satisfies the simple recursive formula that we implemented in the programming language Python 3.4. For inequal boxes and inequal balls we used permutations and combinations together with some results from cases with equal boxes and inequal balls, while the problem with equal balls was more complex and inclusion-exclusion and generating function formulas were needed. The result is a link with the number of injections, surjections and functions, and also the formula for Stirling number of the second kind and Bell’s number. In the end, the results are shown in a table.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:224246
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-09-04 09:09:49