Article
| Title: | Linear preserver of $n\times 1$ Ferrers vectors (English) |
| Author: | Fazlpar, Leila |
| Author: | Armandnejad, Ali |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1189-1200 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $A=[a_{ij}]_{m\times n}$ be an $m\times n$ matrix of zeros and ones. The matrix $A$ is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero $(1,1)$-entry. We characterize all linear maps perserving the set of $n\times 1$ Ferrers vectors over the binary Boolean semiring and over the Boolean ring $\mathbb {Z}_2$. Also, we have achieved the number of these linear maps in each case. (English) |
| Keyword: | Ferrers matrix |
| Keyword: | linear preserver |
| Keyword: | Boolean semiring |
| MSC: | 05B20 |
| MSC: | 15A04 |
| idZBL: | Zbl 07790568 |
| DOI: | 10.21136/CMJ.2023.0440-22 |
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| Date available: | 2023-11-23T12:25:29Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151954 |
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| Reference: | [1] Beasley, L. B.: $(0,1)$-matrices, discrepancy and preservers.Czech. Math. J. 69 (2019), 1123-1131. Zbl 07144881, MR 4039626, 10.21136/CMJ.2019.0092-18 |
| Reference: | [2] Kuich, W., Salomaa, A.: Semirings, Automata, Languages.EATCS Monographs on Theoretical Computer Science 5. Springer, Berlin (1986). Zbl 0582.68002, MR 0817983, 10.1007/978-3-642-69959-7 |
| Reference: | [3] Motlaghian, S. M., Armandnejad, A., Hall, F. J.: Linear preservers of row-dense matrices.Czech. Math. J. 66 (2016), 847-858. Zbl 1413.15051, MR 3556871, 10.1007/s10587-016-0296-4 |
| Reference: | [4] Motlaghian, S. M., Armandnejad, A., Hall, F. J.: Strong linear preservers of dense matrices.Bull. Iran. Math. Soc. 44 (2018), 969-976. Zbl 1407.15003, MR 3846382, 10.1007/s41980-018-0063-4 |
| Reference: | [5] Sirasuntorn, N., Sombatboriboon, S., Udomsub, N.: Inversion of matrices over Boolean semirings.Thai J. Math. 7 (2009), 105-113. Zbl 1201.15002, MR 2540688 |
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