Discrete truncated powers and lattice points in rational polytope.
type: Item
instance of: scholarly article
title: Discrete truncated powers and lattice points in rational polytope.
zbMATH Open document ID: 1090.11064
DOI: 10.1016/S0377-0427(03)00561-2
author: Zhiqiang Xu
author: Ren-Hong Wang
published in: Journal of Computational and Applied Mathematics
publication date: 2003-10-15T00:00:00Z
review text: Es bezeichnen \(\mathbb Z_+,\mathbb R_+\) die Mengen der nicht-negativen ganzen beziehungsweise rationalen Zahlen. Es sei \(M\) eine Matrix, bestehend aus \(s\) Zeilen und \(n\) Spalten, deren Spaltenvektoren aus \(\mathbb Z^s\setminus\{0\}\) genommen sind. Die Gleichung \(M\vec x =\vec 0\) mit \(\vec x\in \mathbb R^n_+\) besitze nur den Nullvektor als Lösung. Untersucht werden die Eigenschaften der Mengen \(t(\alpha|M)=\#\{\beta\in\mathbb Z^n_+:M\beta=\alpha\}\) und gewisser Verallgemeinerungen. Anwendungen werden gegeben auf das Problem der Bestimmung der Anzahl der ganzzahligen Lösungen linearer diophantischer Ungleichungen.
Mathematics Subject Classification ID: 11P21
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 11D75
Mathematics Subject Classification ID: 11D45
zbMATH DE Number: 1993209
zbMATH Keywords: discrete truncated power
zbMATH Keywords: rational polytope
zbMATH Keywords: multivariate spline
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993209