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There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

Set covering deployment (sometimes written "set-covering deployment" and abbreviated SCDP for "set covering deployment problem") seeks an optimal stationing of troops in a ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...