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master's thesis
Particije Rogers-Ramanujanovog tipa
2019. urn:nbn:hr:126:210776
Petrić, Ines
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Petrić, I. (2019). Particije Rogers-Ramanujanovog tipa (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:210776

Petrić, Ines. "Particije Rogers-Ramanujanovog tipa." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:210776

Petrić, Ines. "Particije Rogers-Ramanujanovog tipa." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:210776

Petrić, I. (2019). 'Particije Rogers-Ramanujanovog tipa', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 18 October 2024, https://urn.nsk.hr/urn:nbn:hr:126:210776

Petrić I. Particije Rogers-Ramanujanovog tipa [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 October 18] Available at: https://urn.nsk.hr/urn:nbn:hr:126:210776

I. Petrić, "Particije Rogers-Ramanujanovog tipa", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:210776

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Metadata
TitleParticije Rogers-Ramanujanovog tipa
Title (english)Partitions of the Rogers-Ramanujan Type
AuthorInes Petrić
MentorIvica Martinjak (mentor)
Committee memberDomagoj Ševerdija (predsjednik povjerenstva)
Committee memberIvica Martinjak (član povjerenstva)
Committee memberIvan Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2019-02-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavimo se particijama Rogers-Ramanujanovog tipa. Particija broja n je rastav od n na sumande, gdje poredak nije važan. Particije grafički reprezentiramo pomoću Youngovog dijagrama i taj prikaz koristimo za dokazivanje identiteta za particijsku funkciju. Broj particija čiji su svi dijelovi neparni jednak je broju particija čiji su svi dijelovi medusobno različiti. Lijeva strana prvog i drugog Rogers-Ramanujanovog identiteta je funkcija izvodnica za 2-različite i 2-različite particije s uvjetom da je najmanji dio veći ili jednak od 2. Takve particije nazivamo particije Rogers-Ramanujanovog tipa. Omjer brojeva particija Rogers-Ramanujanovog tipa teži prema zlatnom rezu. Broj particija čija je apsolutna vrijednost razlike izmedu dva dijela veća ili jednaka od 2 jednak je broju particija kod kojih je najmanji parni dio, ukoliko postoji, dvostruko veći od broja neparnih dijelova te particije. Particije s tim svojstvima su poznate kao Rogers-Ramanujanove i polarizirane particije.
Abstract (english)
In this paper we are dealing with partitions of the Rogers-Ramanujan’s type. The partition of n is an decomposition of n on sumande, where order is not important. Partitions are graphically displayed using Young diagram and we use this view to prove the identities for the partition function. The number of partitions whose parts are odd is equal to the number of partitions whose parts are distinct. The left side of the first and second RogersRamanujan’s identity is the 2-distinct and 2-distinct partition with the condition that the smallest part is greater or equal than 2. Such partitions are called the Rogers-Ramanujan type partitions. We observe the ratio of Rogers-Ramanujan’s partitions, where it is known that this ratio actually tends to the golden ratio. The number of 2-distinct partitions is equal to the number of 1-distant partitions whose the smallest even part, if there are any, are greater than twice the number of odd parts. Partitions with these properties are known as Rogers-Ramanujan’s and polarized partitions
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:210776
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
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Created on2019-02-11 11:33:18