본문 바로가기
KERD
논문KCI 등재

Applications of Euler-Seidel matrices

V. Kurt|A. Dil
장전수학회 (Jangjeon Mathematical Society)|2009.04|Advanced Studies in Contemporary Mathematics|제18권 제2호|pp. 219-233

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Fibonacci numbersLucas numbers.Euler- Seidel matrices
주제분류수학

초록

In this paper we give some applications of Euler-Seidel matrices. We use the algorithm method to investigate structures of Fibonacci and Lucas num- bers. We also proved that p (p - 1) + 1 - th row of the Euler-Seidel matrices over Zp (p is prime) is either zero sequence or it repeats the initial sequence.

Abstract

In this paper we give some applications of Euler-Seidel matrices. We use the algorithm method to investigate structures of Fibonacci and Lucas num- bers. We also proved that p (p - 1) + 1 - th row of the Euler-Seidel matrices over Zp (p is prime) is either zero sequence or it repeats the initial sequence.

참고문헌 (18)

  1. T. M. Apostol, "Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics" (1985), Springer-Verlag
  2. L. Comtet, "Advanced Combinatorics in The Art of Finite and Infinite Expansions" (1974), D. Riedel Publishing Co.
  3. J. H. Conway, "The book of numbers" (1996), Springer-Verlag
  4. A. Dil, "Mean Values of Dedekind Sums (in Turkish)", 석사, Mathematics, pp.2005
  5. A. Dil, "Algorithms for Bernoulli and Allied Polynomials", J. Integer Seq., 10 (2007)
  6. A. Dil, "A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers", Applied Mathematics and Computation, 206, pp.942~951 (2008)
  7. D. Dumont, "Matrices d’Euler-Seidel", Seminaire Lotharingien de Combinatorie (1981)
  8. D. Dumont, "A combinatorial interpretation of Seidel generation of Genocchi numbers", Ann. Discrete Math., 6, pp.77~87 (1980)
  9. L. Euler, "De transformatione serierum, Opera Omnia", series prima, 10 (1913)
  11. T. Koshy, "Fibonacci and Lucas Numbers with Applications" (2001), John Wiley and Sons
  12. I. Mezo, "Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence in Central European Journal of Mathematics", ~
  13. N. E. Nörlund, "Mémoire sur les polynômes de Bernoulli", Acta Math., 43, pp.121~196 (1922)
  14. N. E. Nörlund, "Vorlesungen Über Differenzenrechnung" (1954), Chelsea
  15. L. Seidel, "Über eine einfache Enstehung weise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsberichte der Münch. Akad. Math. Phys. Classe", 157~187 (1877)
  16. N. N. Vorobyov, "The Fibonacci Numbers" (1963), D. C. Heath and Company
  17. "Lucas Number"[URL]
  18. H. S. Wilf, "Generatingfunctionology" (1994), Academic Press

관련 논문AI추천

Some properties of the generalized Fibonacci sequence $\{q_n\}$ by matrix methods전상표, 최광호강원경기수학회 · 한국수학논문집2016 · 제24권 제4호THE DIFFERENCE MATRICES OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES김익표장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호Linearlization of generalized Fibonacci sequences장영호, 전상표강원경기수학회 · 한국수학논문집2014 · 제22권 제3호Some Properties of (p, q) - Lucas NumberAlongkot Suvarnamani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial SequencesAlexandre Laugier, Manjil P. Saikia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제1호MODULAR TRIBONACCI NUMBERS BY MATRIX METHOD최은미한국수학교육학회 · 이론수학과 교직수학2013 · 제20권 제3호

이 간행물의 다른 논문 (11건)

New approach to q-Euler, Genocchi numbers and their interpolation functions김태균pp. 105-112A family of hypergeometric integrals associated with Ramanujan's integral formulaH. M. Srivastava, M. I. Qureshi, R. Singh, A. Arorapp. 113-125Symmetry of power sum and twisted Bernoulli polynomials황경원, 김영희pp. 127-133Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functionsV. Kurt, Y. Simsek, M. Cenkci, M. Canpp. 135-160Line semigraph of a semigraphN. S. Bhave, B. Y. Bam, C. M. Deshpandepp. 161-180
원문 보기