Preprint Article Version 1 NOT YET PEER-REVIEWED

Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants

1
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan~Province, China
2
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia Autonomous Region, China
3
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China
4
Department of Mathematics and Informatics, Weinan Teachers University, Weinan 714000, Shaanxi Province, China
5
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo~454010, Henan Province, China
Version 1 : Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:53:07 CEST)

How to cite: Qi, F.; Zhao, J.; Guo, B. Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants. Preprints 2016, 2016100035 (doi: 10.20944/preprints201610.0035.v1). Qi, F.; Zhao, J.; Guo, B. Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants. Preprints 2016, 2016100035 (doi: 10.20944/preprints201610.0035.v1).

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 (1)

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
Commenter's Affiliation: China University
The commenter has declared there is no conflict of interests.
Comment: Nice paper!
+ Respond to this comment
Discuss and rate this article
Views 329
Downloads 163
Comments 1
Metrics 0
Discuss and rate this article

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