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A number n is called k-hyperperfect if n = 1+ksum_(i)d_i (1) = 1+k[sigma(n)-n-1], (2) where sigma(n) is the divisor function and the summation is over the proper divisors ...

An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...

An imperfect graph G is a graph that is not perfect. Therefore, graphs G with omega(G)<chi(G) (1) where omega(G) is the clique number and chi(G) is the chromatic number are ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

The inverse erf function is the inverse function erf^(-1)(z) of the erf function erf(x) such that erf(erf^(-1)(x)) = x (1) erf^(-1)(erf(x)) = x, (2) with the first identity ...

Solving the nome q for the parameter m gives m(q) = (theta_2^4(q))/(theta_3^4(q)) (1) = (16eta^8(1/2tau)eta^(16)(2tau))/(eta^(24)(tau)), (2) where theta_i(q)=theta_i(0,q) is ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...