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The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

Discrete Mathematics

The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

Johnson solid J_(91).

The metric of Felix Klein's model for hyperbolic geometry, g_(11) = (a^2(1-x_2^2))/((1-x_1^2-x_2^2)^2) (1) g_(12) = (a^2x_1x_2)/((1-x_1^2-x_2^2)^2) (2) g_(22) = ...

In elliptic n-space, the pole of an (n-1)-flat is a point located at an arc length of pi/2 radians away from each point of the (n-1)-flat.