On the lattice structure of subsets of octagonal neighborhood sequences in Zn

Authors:
András Hajdu;Lajos Hajdu
Affiliations:
Faculty of Informatics, University of Debrecen, Debrecen, Hungary;Institute of Mathematics, University of Debrecen, and the Number Theory Research Group of the Hungarian Academy of Sciences, Debrecen, Hungary
Venue:
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Year:
2006

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Abstract

In this paper we investigate the lattice properties of several special, but important subsets of Sn, the set of nD octagonal neighborhood sequences in ℤn, with respect to two ordering relations ${\sqsupseteq}$* and $\sqsupseteq$ Both orderings have some natural meaning, especially ${\sqsupseteq}$* compares the ”speed” how neighborhood sequences spread in ℤn We summarize our and the previous related results in a table In particular, our theorems can be considered as extensions of some results from [1,2,3].