Gauss modified pell sayilari üzerine
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Date
2019
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Aksaray Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Özel sayı dizileri ve bu dizilerin genelleştirilmeleri birçok yazar tarafından incelenmiştir. Bu tezin amacı Gauss modified Pell sayı dizisini tanımlamak ve birtakım özelliklerini belirlemektir. Ayrıca bu tanımı kullanarak Gauss modified Pell polinom dizisini ve Gauss (s,t)-modified Pell dizisini tanımlayarak, özelliklerini incelemek amaçlanmaktadır. Bu tez yedi bölümden oluşmaktadır. İlk bölümde, Fibonacci sayı dizisi başta olmak üzere bazı özel sayı dizilerinin tarihçesinden ve günlük hayattaki kullanım alanlarından bahsedildi. İkinci bölümde, çalışmamızda ihtiyaç duyulan temel tanım ve teoremler ifade edildi. Üçüncü bölümde, Gauss modified Pell dizisi tanımlandı ve bazı kombinatoryal özellikleri incelendi. Dördüncü bölümde, Gauss modified Pell polinom dizisi tanımlanarak bazı özellikleri ele alındı. Beşinci bölümde, ilk olarak modified Pell dizisinin bir genelleştirilmesi olan (s,t)-modified Pell dizisi tanımlandı. Daha sonra (s,t)-modified Pell dizisinin elemanlarından oluşan (s,t)-modified Pell matris dizisi tanımlandı. Bu dizilere ait bazı kombinatoryal özellikler incelendi. Altıncı bölümde, Gauss modified Pell dizisinin bir genelleştirilmesi olan Gauss (s,t)-modified Pell dizisi tanımlandı. Sonra Gauss (s,t)-modified Pell dizisinin elemanlarından oluşan Gauss (s,t)-modified Pell matris dizisi tanımlandı. Bu dizilere ait bazı özellikler ele alındı. Son bölümde, tezde elde edilen birtakım sonuçlara ve bazı önerilere yer verildi.
Special number sequences and their generalizations have been studied by many authors. The aim of this thesis is to define Gaussian modified Pell number sequence and to determine some properties of this sequence. Also, by using this definition, it is aimed to define Gaussian modified Pell polynomial sequence and Gaussian (s,t)-modified Pell sequence and to examine some properties of these sequences. This thesis consists of seven chapters. In the first chapter, the history of some special number sequences, especially Fibonacci number sequence, and usage of these number sequences in daily life are mentioned. In the second chapter, some basic concept and definitions needed in the further chapters are given. In the third chapter, the Gaussian modified Pell sequence is defined and some combinatorial properties of this sequence are examined. In the fourth chapter, the Gaussian modified Pell polynomial sequence is defined and some of its properties are discussed. In the fifth chapter, (s,t)-modified Pell sequence which is a generalization of the modified Pell sequence is firstly defined. Then, (s,t)-modified Pell matrix sequence whose components consist of the modified Pell numbers is defined. Some combinatorial properties of these sequences are investigated. In the sixth chapter, Gaussian (s,t)-modified Pell sequence which is a generalization of the Gaussian modified Pell sequence is firstly defined. Then, Gaussian (s,t)-modified Pell matrix sequence whose components consist of the Gaussian modified Pell numbers is defined. Some combinatorial properties of these sequences are discussed. In the last chapter, the main results obtained from the thesis and some proposals are discussed.
Special number sequences and their generalizations have been studied by many authors. The aim of this thesis is to define Gaussian modified Pell number sequence and to determine some properties of this sequence. Also, by using this definition, it is aimed to define Gaussian modified Pell polynomial sequence and Gaussian (s,t)-modified Pell sequence and to examine some properties of these sequences. This thesis consists of seven chapters. In the first chapter, the history of some special number sequences, especially Fibonacci number sequence, and usage of these number sequences in daily life are mentioned. In the second chapter, some basic concept and definitions needed in the further chapters are given. In the third chapter, the Gaussian modified Pell sequence is defined and some combinatorial properties of this sequence are examined. In the fourth chapter, the Gaussian modified Pell polynomial sequence is defined and some of its properties are discussed. In the fifth chapter, (s,t)-modified Pell sequence which is a generalization of the modified Pell sequence is firstly defined. Then, (s,t)-modified Pell matrix sequence whose components consist of the modified Pell numbers is defined. Some combinatorial properties of these sequences are investigated. In the sixth chapter, Gaussian (s,t)-modified Pell sequence which is a generalization of the Gaussian modified Pell sequence is firstly defined. Then, Gaussian (s,t)-modified Pell matrix sequence whose components consist of the Gaussian modified Pell numbers is defined. Some combinatorial properties of these sequences are discussed. In the last chapter, the main results obtained from the thesis and some proposals are discussed.
Description
Keywords
Gauss Modified Pell Sayı Dizisi, Gauss Modified Pell Polinom Dizisi, Gauss (s,t)-modified Pell Matris Dizisi, Gaussian Modified Pell Number Sequence, Gaussian Modified Pell Polynomial Sequence, Gaussian (s,t)-modified Pell Sequence, Gaussian (s,t)- modified Pell Matrix Sequence
