Construction of evidently positive series and an alternative construction for a family of partition generating functions deu to Kanade and Russell

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Ömrüuzun Seyrek, Halime (2021) Construction of evidently positive series and an alternative construction for a family of partition generating functions deu to Kanade and Russell. [Thesis]

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Abstract

Construction of generating functions for partitions, especially construction evidently positive series as generating functions for partitions is a quite interesting problem. Recently, Kurşungöz has been constructed evidently positive series as generating functions for the partitions satisfying the di erence conditions imposed by Capparelli's identities and Göllnitz-Gordon identities, for the partitions satisfying certain di erence conditions in six conjectures by Kanade and Russell and the partitions satisfying the multiplicity condition in Schur's partition theorem. In this thesis, we give an alternative construction for a family of partition generating functions due to Kanade and Russell. In our alternative construction, we use ordinary partitions instead of jagged partitions. We also present new generating functions which are evidently positive series for partitions due to Kanade and Russell. To obtain those generating functions, we rst construct an evidently positive series for a key in nite product. In that construction, a series of combinatorial moves is used to decompose an arbitrary partition into a base partition together with some auxiliary partitions that bijectively record the moves.
Item Type: Thesis
Uncontrolled Keywords: integer partition. -- partition generating function. -- evidently positive generating functions. -- Rogers-Ramanujan type partition identities. -- tam sayı parçalanışı. -- parçalanış üreteç fonksiyonu. -- bariz pozitif üreteç fonksiyonlar. -- Rogers- Ramanujan tipi parçalanış özdeşlikleri.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 12 Nov 2021 15:14
Last Modified: 26 Apr 2022 10:39
URI: https://research.sabanciuniv.edu/id/eprint/42535

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