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The tau conjecture, also known as Ramanujan's hypothesis after its proposer, states that tau(n)∼O(n^(11/2+epsilon)), where tau(n) is the tau function. This was proven by ...

Let G be a group having normal subgroups H and K with H subset= K. Then K/H⊴G/H and (G/H)/(K/H)=G/K, where N⊴G indicates that N is a normal subgroup of G and G=H indicates ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

The Weierstrass constant is defined as the value sigma(1|1,i)/2, where sigma(z|omega_1,omega_2) is the Weierstrass sigma function with half-periods omega_1 and omega_2. ...

The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

An illusion invented by the German psychologist Wilhelm Wundt in the 19th century. In the figure above, the two red horizontal lines are both straight, but they look as if ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...