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master's thesis
Sparivanja i Pfaffian orijentacije
2019. urn:nbn:hr:126:379252
Tešija, Anita
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Computer Science and Machine Learning Research Group

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Tešija, A. (2019). Sparivanja i Pfaffian orijentacije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:379252

Tešija, Anita. "Sparivanja i Pfaffian orijentacije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:379252

Tešija, Anita. "Sparivanja i Pfaffian orijentacije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:379252

Tešija, A. (2019). 'Sparivanja i Pfaffian orijentacije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:379252

Tešija A. Sparivanja i Pfaffian orijentacije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:379252

A. Tešija, "Sparivanja i Pfaffian orijentacije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:379252

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Metadata
TitleSparivanja i Pfaffian orijentacije
Title (english)Matching and Pfaffian Orientation
AuthorAnita Tešija
MentorSnježana Majstorović (mentor)
Committee memberSlobodan Jelić (predsjednik povjerenstva)
Committee memberSnježana Majstorović (član povjerenstva)
Committee memberDomagoj Ševerdija (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Computer Science and Machine Learning Research Group)
Osijek
Defense date and country2019-11-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Pfaffian matrice je u teoriji grafova iznimno važan jer se koristi za prebrojavanje savršenih sparivanja u grafu. Da bi to bilo moguće, nužno je da su grafovi planarni. Zato smo uveli pojam planarnog grafa te pokazali neke osnovne pojmove i tvrdnje o sparivanjima. Za prebrojavanje savršenih sparivanja, koristili smo vezu između determinante i Pfaffiana matrice \(det(B) = (P f(B))^2\) koju je prvi ustanovio Cayley 1849. godine. Kako bi si još olakšali prebrojavanje uvodi se pojam Pfaffian orijentacija, koja naglašava kakva orijentacija mora biti u nekom grafu da bi mogli prebrojavati savršena sparivanja. Jedna od glavnih primjena Pfaffiana dobiva svoj smisao na pravokutnim mrežama, jer su one primjenjive u fizici, gdje ih koristimo kod problema prelazaka dvoatomskog plina u kristalni supstrat.
Abstract (english)
Pfaffian of a matrix is in graph theory very important since it is applicable for counting perfect matchings in a graph. To make this possible, graphs have to be planar. Because of that, we introduced notion of a planar graph and some basic terms and theorems on matching. For counting perfect matching in graphs, we used connection between a determinant of a matrix and its Pfaffian \(det(B) = (P f(B))^2\) which was established by Cayley in 1849. To make it even simple to count, we introduced the term Pfaffian orientation. Which highlights what orientation must be in graph for counting perfect matching. The key applications of Pfaffian is in rectangular grids. Because rectangular grids is applicable in physics, where we use them in the problem of the transition two-atom gas in a crystalline substrate.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:379252
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-11-27 12:03:51