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In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

A d-dimensional discrete percolation model on a regular point lattice L=L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

17 is a Fermat prime, which means that the 17-sided regular polygon (the heptadecagon) is constructible using compass and straightedge (as proved by Gauss).

Baxter's four-coloring constant for a triangular lattice is given by C^2 = product_(j=1)^(infty)((3j-1)^2)/((3j-2)(3j)) (1) = 3/(4pi^2)Gamma^3(1/3) (2) = 1.46099848... (3) ...

A figurate number in which layers of polygons are drawn centered about a point instead of with the point at a polygon vertex.

A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...

A concordance between knots K_0 and K_1 in S^3 is a locally flat cylinder C=S^1×[0,1] embedded in S^3×[0,1] in such a way that the ends S^1×{1} are embedded in S^3×{i} as ...

A functor F is called contravariant if it reverses the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(B)-->F(A).