On a matrix partition conjecture
| Autor: | Dale M. Mesner, Earl S. Kramer, Stephen Mellendorf, Richard A. Brualdi, Peter Horak, Geňa Hahn |
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| Rok vydání: | 1995 |
| Předmět: |
T matrix
Conjecture 010102 general mathematics Block matrix 0102 computer and information sciences Partition matrix 01 natural sciences Theoretical Computer Science Combinatorics Matrix (mathematics) Computational Theory and Mathematics 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Order (group theory) 0101 mathematics Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 69:333-346 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/0097-3165(95)90056-x |
| Popis: | In 1977, Ganter and Teirlinck proved that any 2 t × 2 t matrix with 2 t nonzero elements can be partitioned into four submatrices of order t of which at most two contain nonzero elements. In 1978, Kramer and Mesner conjectured that any mt × nt matrix with kt nonzero elements can be partitioned into mn submatrices of order t of which at most k contain nonzero elements. We show that this conjecture is true for some values of m , n , t and k but that it is false in general. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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