Preprint Article Version 1 This version not peer reviewed

Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants

Version 1 : Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:53:07 CEST)

A peer-reviewed article of this Preprint also exists.

Journal reference: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales--Serie A: Matematicas 2017
DOI: 10.1007/s13398-017-0401-z

Abstract

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

Subject Areas

derangement number; closed form; Hessenberg determinant; tridiagonal determinant; generating function; recurrence relation; derivative

Readers' Comments and Ratings (3)

Importance: How significant is the paper to the field?
Outstanding/highlight paper
0%
Significant contribution
100%
Incremental contribution
0%
No contribution
0%
Soundness of evidence/arguments presented:
Conclusions well supported
100%
Most conclusions supported (minor revision needed)
0%
Incomplete evidence (major revision needed)
0%
Hypothesis, unsupported conclusions, or proof-of-principle
0%
Comment 1
Received: 18 October 2016
Commenter: Honest John China
The commenter has declared there is no conflict of interests.
Comment: Nice paper!
+ Respond to this comment
Comment 2
Received: 13 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the corresponding author of this paper.
Comment: This preprint will be formally published as follows.

Feng Qi, Jiao-Lian Zhao, and Bai-Ni Guo, Closed forms for derangement numbers in terms of the Hessenberg determinants, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 112 (2018), in press; Available online at http://dx.doi.org/10.1007/s13398-017-0401-z.
+ Respond to this comment
Comment 3
Received: 20 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this paper.
Comment: Sharing Information for “Closed forms for derangement numbers in terms of the Hessenberg determinants”

Dear Author,

Congratulations on publishing “Closed forms for derangement numbers in terms of the Hessenberg determinants” in Revista de la Real Academia de Ciencias Exactas, Físicas y. As part of the Springer Nature SharedIt initiative, you can now publicly share a full-text view-only version of your paper by using the link below. If you have selected an Open Access option for your paper, or where an individual can view content via a personal or institutional subscription, recipients of the link will also be able to download and print the PDF. All readers of your article via the shared link will also be able to use Enhanced PDF features such as annotation tools, one-click supplements, citation file exports and article metrics.

http://rdcu.be/rWH4
We encourage you to forward this link to your co-authors, as sharing your paper is a great way to improve the visibility of your work. There are no restrictions on the number of people you may share this link with, how many times they can view the linked article or where you can post the link online.

More information on Springer Nature’s commitment to content sharing is available here.

Sincerely,
Springer Nature
+ Respond to this comment
Leave a public comment
Send a private comment to the author(s)
Rate this article
Views 0
Downloads 0
Comments 3
Metrics 0
Leave a public comment

×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.