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Pascal-like determinants are recursive
Zakrajšek, Helena ; Petkovšek, Marko, 1955-2023
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.
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