p^(k)-Fibonacci Numbers of the p-Bratteli Diagram for Every Odd Prime p and Integer k>=0
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914368618233856 |
|---|---|
| author | Parvathi, M. Tamilselvi, A. Hepsi, D. |
| author_facet | Parvathi, M. Tamilselvi, A. Hepsi, D. |
| contents | We study paths in the p-Bratteli diagram associated with hook partitions, where p is an odd prime. By comparing blocks along a path, we define inversions and descents. We prove that the sign balance derived from inversions vanishes at every vertex of the diagram. Using descents, we introduce the p^(k)-Fibonacci numbers and derive recurrence relations for them. For k=0, we recover the OEIS sequence A391520, while for k>=1 we obtain new families of Fibonacci-type sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04229 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | p^(k)-Fibonacci Numbers of the p-Bratteli Diagram for Every Odd Prime p and Integer k>=0 Parvathi, M. Tamilselvi, A. Hepsi, D. Combinatorics Primary: 05E10, Secondary: 05A15, 05E16 We study paths in the p-Bratteli diagram associated with hook partitions, where p is an odd prime. By comparing blocks along a path, we define inversions and descents. We prove that the sign balance derived from inversions vanishes at every vertex of the diagram. Using descents, we introduce the p^(k)-Fibonacci numbers and derive recurrence relations for them. For k=0, we recover the OEIS sequence A391520, while for k>=1 we obtain new families of Fibonacci-type sequences. |
| title | p^(k)-Fibonacci Numbers of the p-Bratteli Diagram for Every Odd Prime p and Integer k>=0 |
| topic | Combinatorics Primary: 05E10, Secondary: 05A15, 05E16 |
| url | https://arxiv.org/abs/2603.04229 |