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Pascal-like determinants are recursiveZakrajšek, Helena, 1965- ; Petkovšek, Marko, 1955-Naj bo ▫$P=[p_{i,j}]_{i,j \ge 0}$▫ neskončna matrika, katere elementi za ▫$i,j \ge 1$▫ zadoščajo rekurzivni enačbi ▫$p_{i,j} = \mu p_{i,j-1} + \lambda p_{i-1,j} +\ni p_{i-1,j-1$▫, medtem ko elementi ... prvega stolpca oziroma prve vrstice zadoščajo linearni rekurzivni enačbi reda ▫$\rho$▫ oziroma ▫$\sigma$▫ s konstantnimi koeficienti. Potem njeni glavni minorji ▫$d_n$▫ zadoščajo rekurzivni enačbi ▫$d_n = \sum_{j=1}^\delta c_j\omega^{jn} d_{n-j}$▫, kjer so ▫$c_j$▫ konstante, ▫$\omega = \lambda\mu + \nu$▫ in ▫$\delta = {\rho+\sigma-2 \choose \rho-1}$▫. Od tod sledi veljavnost nedavne domneve R. Bacherja.Source: Advances in applied mathematics. - ISSN 0196-8858 (Vol. 33, no. 3, 2004, str. 431-450)Type of material - article, component partPublish date - 2004Language - englishCOBISS.SI-ID - 13210713
Author
Zakrajšek, Helena, 1965- |
Petkovšek, Marko, 1955-
Topics
determinanta |
Pascalovi podobna matrika |
linearna rekurzivna enačba s konstantnimi koeficienti |
pasovna matrika |
matrična rodovna funkcija |
glavni minor |
determinant |
Pascal-like matrix |
linear recurrence with constant coefficients |
band-diagonal matrix |
matrix generating function |
principal minor
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Zakrajšek, Helena, 1965- | 21773 |
Petkovšek, Marko, 1955- | 01935 |
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