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Oriented Lattice


An oriented lattice is a point lattice L equipped with a graph structure and a rule assigning a direction to each edge connecting lattice points. In that way, an oriented lattice is intimately connected to an oriented graph.

Given a point lattice L with edges joining nearest neighbors along the coordinate axes, one common such rule is the so-called north-east rule, which directs each edge in the direction of increasing coordinate value. This type of oriented lattice is central in a number of fields, e.g., in oriented percolation models within the field of discrete percolation theory.


See also

Bond Percolation, Bootstrap Percolation, Continuum Percolation Theory, Percolation, Percolation Theory, Percolation Threshold, Site Percolation

Portions of this entry contributed by Christopher Stover

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References

Grimmett, G. Percolation, 2nd ed. Berlin, Germany: Springer-Verlag, 1999.

Referenced on Wolfram|Alpha

Oriented Lattice

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Oriented Lattice." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OrientedLattice.html

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