Harmonic numbers associated with inversion numbers in terms of determinants

Authors

TAKAO KOMATSU
Amalia Pizarro-Madariaga

Abstract

It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers 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 concepts can be generalized in the case of hyperharmonic numbers.

DOI

10.3906/mat-1809-52

Keywords

Harmonic numbers, hyperharmonic numbers, recurrence relations, determinants, convolutions

First Page

340

Last Page

354

Recommended Citation

KOMATSU, TAKAO and Pizarro-Madariaga, Amalia (2019) "Harmonic numbers associated with inversion numbers in terms of determinants," Turkish Journal of Mathematics: Vol. 43: No. 1, Article 27. https://doi.org/10.3906/mat-1809-52
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/27