On the Lattice Structure of Subsets of Octagonal Neighborhood Sequences in ℤn

  • András Hajdu
  • Lajos Hajdu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


In this paper we investigate the lattice properties of several special, but important subsets of S n , 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].


Lattice Structure Distributive Lattice Lattice Property Period Length Periodic Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • András Hajdu
    • 1
  • Lajos Hajdu
    • 2
  1. 1.Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.Institute of MathematicsUniversity of Debrecen, and the Number Theory Research Group of the Hungarian Academy of SciencesDebrecenHungary

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