VERIFYING AND GENERALIZING ARNDT’S COMPOSITIONS
1
Issued Date
2022-12-01
Resource Type
ISSN
00150517
Scopus ID
2-s2.0-85166150733
Journal Title
Fibonacci Quarterly
Volume
60
Issue
5
Start Page
181
End Page
186
Rights Holder(s)
SCOPUS
Bibliographic Citation
Fibonacci Quarterly Vol.60 No.5 (2022) , 181-186
Suggested Citation
Hopkins B., Tangboonduangjit A. VERIFYING AND GENERALIZING ARNDT’S COMPOSITIONS. Fibonacci Quarterly Vol.60 No.5 (2022) , 181-186. 186. doi:10.1080/00150517.2022.12427438 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/101663
Title
VERIFYING AND GENERALIZING ARNDT’S COMPOSITIONS
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Abstract
In 2013, Joerg Arndt recorded that the Fibonacci numbers count integer compositions where the first part is greater than the second, the third part is greater than the fourth, etc. We provide two combinatorial proofs that verify his observation. Also, we generalize the descent condition and establish families of recurrence relations. Compositions with parts restricted to 1 and 2 play an important role.