The Fibonacci-Fubini and Lucas-Fubini numbers
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916313515950080 |
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| author | Djemmada, Yahia Mehdaoui, Abdelghani Németh, László Szalay, László |
| author_facet | Djemmada, Yahia Mehdaoui, Abdelghani Németh, László Szalay, László |
| contents | Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define the Fibonacci-Fubini numbers that count the total number of Fibonacci partitions of $[n]$. We study the classical properties of this sequence (generating function, explicit and Dobiński-like formula, etc.), we give combinatorial interpretation, and we extensively examine the Fibonacci-Fubini arithmetic triangle. We give some associate linear recurrence sequences, where in some sequences the Stirling numbers of the first and second kinds appear as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Fibonacci-Fubini and Lucas-Fubini numbers Djemmada, Yahia Mehdaoui, Abdelghani Németh, László Szalay, László Combinatorics Number Theory 05A15, 05A18, 11B39, 11B37, 11B73 Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define the Fibonacci-Fubini numbers that count the total number of Fibonacci partitions of $[n]$. We study the classical properties of this sequence (generating function, explicit and Dobiński-like formula, etc.), we give combinatorial interpretation, and we extensively examine the Fibonacci-Fubini arithmetic triangle. We give some associate linear recurrence sequences, where in some sequences the Stirling numbers of the first and second kinds appear as well. |
| title | The Fibonacci-Fubini and Lucas-Fubini numbers |
| topic | Combinatorics Number Theory 05A15, 05A18, 11B39, 11B37, 11B73 |
| url | https://arxiv.org/abs/2407.04409 |