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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

Harmonic numbers associated with inversion numbers in terms of determinants

Takao KOMATSU
Amalia PIZARRO MADARIAGA
Sayfa
340–354
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

These conceptscan be generalized in the case of hyperharmonic numbers.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such correspondingnumbers in terms of determinants of Hessenberg matrices.
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Temel Bulgular & Veri:There exist inversion relations between the originalnumbers and the corresponding numbers.
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Sonuç & Katkı:These conceptscan be generalized in the case of hyperharmonic numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such correspondingnumbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the originalnumbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants.We also give several of their arithmetical and/or combinatorial properties and applications. These conceptscan be generalized in the case of hyperharmonic numbers.

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Bu Makaleye Atıf Yap

KOMATSU, T., MADARIAGA, A. P. (2022). Harmonic numbers associated with inversion numbers in terms of determinants. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 340–354. https://ajindex.com/articles/607721

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Kaynakça (21)

  1. Agoh T, Dilcher K. Convolution identities and lacunary recurrences for Bernoulli numbers. J Number Theory 2007; 124: 105-122
  2. Brioschi F. Sulle funzioni Bernoulliane ed Euleriane. Annali de Mat 1858; 1: 260-263 (in Italian)
  3. Cameron PJ. Some sequences of integers. Discrete Math 1989; 75: 89-102
  4. Chu W. Summation formulae involving harmonic numbers. Filomat 2012; 26: 143-152
  5. Comtet L. Advanced Combinatorics. Dordrecht, the Netherlands: Reidel, 1974
  6. Glaisher JWL. Expressions for Laplace’s coefficients, Bernoullian and Eulerian numbers etc. as determinants. Messenger 1875; 6: 49-63
  7. Gross OA. Preferential arrangements. Am Math Mon 1962; 69: 4-8
  8. Komatsu T. Complementary Euler numbers. Period Math Hungar 2017; 75: 302-314
  9. Komatsu T, Mező I, Szalay L. Incomplete Cauchy numbers. Acta Math Hungar 2016; 149: 306-323
  10. Komatsu T, Ohno Y. Lehmer’s generalized Euler numbers. Preprint
  11. Komatsu T, Ramirez JL. Some determinants involving incomplete Fubini numbers. An Ştiinţ Univ “Ovidius” Constanţa Ser Mat 2018; 26: 143-170
  12. Komatsu T, Yuan P. Hypergeometric Cauchy numbers and polynomials. Acta Math Hungar 2017; 153: 382-400
  13. Kronenburg MJ. On two types of Harmonic number identities. arXiv:1202.3981, 2012
  14. Lehmer DH. Lacunary recurrence formulas for the numbers of Bernoulli and Euler. Ann Math 1935; 36: 637-649
  15. Mező I. Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions. Cent Eur J Math 2013; 11: 931-939
  16. Mező I, Dil A. Hyperharmonic series involving Hurwitz zeta function. J Number Theory 2010; 130: 360-369
  17. Muir T. The Theory of Determinants in the Historical Order of Development. Four Volumes. New York, NY, USA: Dover Publications, 1960
  18. Polya G. Induction and Analogy in Mathematics. Princeton, NJ, USA: Princeton University Press, 1954
  19. Sloane NJA. The On-line Encyclopedia of Integer Sequences. Available at www.oeis.org, 2017
  20. SpießJ. Some identities involving harmonic numbers. Math Comp 1990; 55: 839-863
  21. Trudi N. Intorno ad alcune formole di sviluppo. Rendic dell’ Accad Napoli 1862: 135-143 (in Italian).