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Oriented Lattice


A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an oriented lattice is intimately connected to an oriented graph.

Given a point lattice L, one common such rule is the so-called north-east rule which orients each edge of L in the direction of increasing coordinate-value. This type of ordered 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

This entry contributed by Christopher Stover

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References

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

Cite this as:

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

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