Authors: Acketa, Dragan
Žunić, Joviša 
Title: On the number of linear partitions of the (m, n)-grid
Journal: Information Processing Letters
Volume: 38
Issue: 3
First page: 163
Last page: 168
Issue Date: 17-May-1991
ISSN: 0020-0190
DOI: 10.1016/0020-0190(91)90240-I
Abstract: 
A relationship between linear partitions and minimal pairs of a finite point set in the plane was established in [2]. This relationship is used here for counting the number of linear partitions of the set of points of the (m, n)-grid, a rectangular part of the infinite grid. In order to optimize this counting, an O(mn) algorithm is introduced for traversing all those pairs (i, j) of mutually simple natural numbers i and j, such that 1 ≤i≤m, 1≤j≤n.
Keywords: (m,n)-grids in the plane | computational complexity | Computational geometry | linear partitions | point sets
Publisher: Elsevier

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