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

  • András Hajdu
  • Lajos Hajdu
Conference paper
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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