Scanning integer matrices by means of two rectangular windows

Authors:
Andrea Frosini;Maurice Nivat;Simone Rinaldi
Affiliations:
Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, V.le Morgagni, 65, 50134, Firenze, Italy;Laboratoire dInformatique, Algorithmique, Fondements et Applications (LIAFA), Université Denis Diderot 2, place Jussieu 75251 Paris Cedex 05, France;Dipartimento di Scienze Matematiche ed Informatiche Roberto Magari Università degli Studi di Siena, Pian dei Mantellini 44, 53100, Siena, Italy
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

This paper deals with the reconstruction of integer matrices from rectangular scans. In particular, since the case of one rectangular scan has already been treated in a previous paper, we consider two rectangular scans, given as two integer matrices, and we investigate the existence and the possibility of reconstruction of a third binary matrix which is compatible with them. Furthermore, our inspection implies interesting side results about the number of these reconstructed matrices for different choices of the dimensions of two windows used in the input scans.