Preprint Article Version 1 NOT YET PEER-REVIEWED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 179
Downloads 68
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.