Article
| Title: | Additive decomposition of matrices under rank conditions and zero pattern constraints (English) |
| Author: | Bart, Harm |
| Author: | Ehrhardt, Torsten |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 825-854 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | This paper deals with additive decompositions $A=A_1+\cdots +A_p$ of a given matrix $A$, where the ranks of the summands $A_1,\ldots , A_p$ are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs. (English) |
| Keyword: | additive decomposition |
| Keyword: | rank constraint |
| Keyword: | zero pattern constraint |
| Keyword: | directed bipartite graph |
| Keyword: | $ß{L}$-free directed bipartite graph |
| Keyword: | permutation $ß{L}$-free directed bipartite graph |
| Keyword: | Bell number |
| Keyword: | Stirling partition number |
| MSC: | 05C20 |
| MSC: | 05C50 |
| MSC: | 15A03 |
| MSC: | 15A21 |
| idZBL: | Zbl 07584105 |
| idMR: | MR4467945 |
| DOI: | 10.21136/CMJ.2022.0185-21 |
| . | |
| Date available: | 2022-08-22T08:24:45Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150620 |
| . | |
| Reference: | [1] Bart, H., Ehrhardt, T., Silbermann, B.: Rank decomposition in zero pattern matrix algebras.Czech. Math. J. 66 (2016), 987-1005. Zbl 1413.15010, MR 3556880, 10.1007/s10587-016-0305-7 |
| Reference: | [2] Bart, H., Ehrhardt, T., Silbermann, B.: Echelon type canonical forms in upper triangular matrix algebras.Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics Operator Theory: Advances and Applications 259. Birkhäuser, Basel (2017), 79-124. Zbl 1365.15014, MR 3644514, 10.1007/978-3-319-49182-0_8 |
| Reference: | [3] Bart, H., Ehrhardt, T., Silbermann, B.: $ß{L}$-free directed bipartite graphs and echelon-type canonical forms.Operator Theory, Analysis and the State Space Approach Operator Theory: Advances and Applications 271. Birkhäuser, Cham (2018), 75-117. Zbl 1427.15016, MR 3889652, 10.1007/978-3-030-04269-1_3 |
| Reference: | [4] Bart, H., Ehrhardt, T., Silbermann, B.: Rank decomposition under zero pattern constraints and $ß{L}$-free directed graphs.Linear Algebra Appl. 621 (2021), 135-180. Zbl 1464.15002, MR 4231570, 10.1016/j.laa.2021.03.010 |
| Reference: | [5] Bart, H., Wagelmans, A. P. M.: An integer programming problem and rank decomposition of block upper triangular matrices.Linear Algebra Appl. 305 (2000), 107-129. Zbl 0951.15013, MR 1733797, 10.1016/S0024-3795(99)00219-0 |
| Reference: | [6] Birkhoff, G.: Lattice Theory.American Mathematical Society Colloquium Publications 25. AMS, Providence (1967). Zbl 0153.02501, MR 0227053, 10.1090/coll/025 |
| Reference: | [7] Charalambides, C. A.: Enumerative Combinatorics.CRC Press Series on Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2002). Zbl 1001.05001, MR 1937238, 10.1201/9781315273112 |
| Reference: | [8] Habib, M., Jegou, R.: $N$-free posets as generalizations of series-parallel posets.Discrete Appl. Math. 12 (1985), 279-291. Zbl 0635.06002, MR 0813975, 10.1016/0166-218X(85)90030-7 |
| Reference: | [9] Riordan, J.: Combinatorial Identities.John Wiley & Sons, New York (1968). Zbl 0194.00502, MR 0231725 |
| Reference: | [10] Stanley, R. P.: Enumerative Combinatorics. Vol. 1.Cambridge Studies in Advanced Mathematics 49. Cambridge University Press, Cambridge (1997). Zbl 0889.05001, MR 1442260, 10.1017/CBO9780511805967 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
