Grayevi kodovi

master's thesis

• Title (english): Gray codes
• Author: Ivona Uzelac
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-12-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES

Abstract

Tema ovog diplomskog rada su Grayevi kodovi, odnosno metode generiranja kombinatornih objekata takvih da se susjedni objekti razlikuju na neki unaprijed određen način ili, najčešće, minimalno. Prema patentu Franka Graya defnirali smo Grayev kod za binarne nizove i za podskupove nekog skupa. Istu ideju primijenili smo i na druge kombinatorne objekte: kombinacije, permutacije i particije. Uz Grayev kod za permutacije defnirali smo dodatno i kod koji mu je suprotan, odnosno u kojem se susjedne permutacije razlikuju na svim mjestima. Algoritme za generiranje defniranih Grayevih kodova implementirali smo u programskom jeziku Python.

Abstract (english)

The topic of this thesis are Gray codes: methods for generating combinatorial objects so that successive objects differ in some pre-speciffed way or, most often, minimally. According to Frank Gray's patent, we deffned Gray codes for binary arrays and for subsets of a set. We applied the same idea to other combinatorial objects: combinations, permutations, and partitions. In addition to Gray co- des for permutations, we have deffned a code that is opposite to it, i.e. in which adjacent permutations differ in all places. We have implemented algorithms for generating Gray codes in the Python programming language.

• Keywords: Frank Gray; Grayev kod za binarne nizove; programski jezik Python
• Keywords (english): Frank Gray's patent; Gray codes for binary arrays; Python programming language
• Language: croatian
• URN:NBN: urn:nbn:hr:217:466871
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-02-24 13:47:17