期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：2-3
页码：229-237
DOI：10.1016/j.akcej.2015.11.020
语种：English
出版社：Elsevier
摘要：AbstractThe aim of this work is to provide a complete characterization of a(m,n)-cube. The latter are the pieces of discrete planes appearing in Theoretical Computer Science, Discrete Geometry and Combinatorics. This characterization in three dimensions is the exact equivalent of the preimage for a discrete segment as it has been introduced by McIlroy. Further this characterization, which avoids the redundancies, reduces the combinatorial problem of determining the cardinality of the(m,n)-cubes to a new combinatorial problem consisting of determining the volumic regions formed by the crossing of planes. This work can find applications in Imaging, Vision, and pattern recognition for instance.
关键词：KeywordsenCombinatorial number theoryFarey diagramsTheoretical computer sciencesDiscrete planesDiscrete geometry
