Group inverses of $\{0,1\}$-triangular matrices and Fibonacci numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866912284320727040 |
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| author | Chatterjee, Manami Sivakumar, K. C. |
| author_facet | Chatterjee, Manami Sivakumar, K. C. |
| contents | A number $s$ is the sum of the entries of the inverse of an $n \times n, (n \geq 3)$ upper triangular matrix with entries from the set $\{0, 1\}$ if and only if $s$ is an integer lying between $2-F_{n-1}$ and $2+F_{n-1}$, where $F_n$ is the $n$th Fibonacci number. A generalization of the sufficient condition above to singular, group invertible matrices is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_11927 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Group inverses of $\{0,1\}$-triangular matrices and Fibonacci numbers Chatterjee, Manami Sivakumar, K. C. Combinatorics 15A09, 15B36 A number $s$ is the sum of the entries of the inverse of an $n \times n, (n \geq 3)$ upper triangular matrix with entries from the set $\{0, 1\}$ if and only if $s$ is an integer lying between $2-F_{n-1}$ and $2+F_{n-1}$, where $F_n$ is the $n$th Fibonacci number. A generalization of the sufficient condition above to singular, group invertible matrices is presented. |
| title | Group inverses of $\{0,1\}$-triangular matrices and Fibonacci numbers |
| topic | Combinatorics 15A09, 15B36 |
| url | https://arxiv.org/abs/2005.11927 |