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

Harmonic numbers associated with inversion numbers in terms of determinants

Takao KOMATSU
Amalia PIZARRO MADARIAGA
Pages
340–354
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These conceptscan be generalized in the case of hyperharmonic numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such correspondingnumbers in terms of determinants of Hessenberg matrices.
📊
Key Findings & Data:There exist inversion relations between the originalnumbers and the corresponding numbers.
💡
Conclusion & Impact:These conceptscan be generalized in the case of hyperharmonic numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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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Cite This Article

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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