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Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

Let C be an error-correcting code consisting of N codewords,in which each codeword consists of n letters taken from an alphabet A of length q, and every two distinct ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

A set of residues {a_1,a_2,...,a_(k+1)} (mod n) such that every nonzero residue can be uniquely expressed in the form a_i-a_j. Examples include {1,2,4} (mod 7) and {1,2,5,7} ...

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., omega(G)=chi(G). A graph that is not a perfect ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...