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A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the ...

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A method for constructing magic squares of odd order, also called the Siamese method.

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...

The first quadratic nonresidue mod p of a number is always less than 3(lnp)^2/2 (Wedeniwski 2001).

If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...