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The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

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 triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

The Euler-Mascheroni constant gamma, sometimes also called 'Euler's constant' or 'the Euler constant' (but not to be confused with the constant e=2.718281...) is defined as ...

Wyler's constant is defined as alpha_W = 9/(8pi^4)((pi^5)/(2^4·5!))^(1/4) (1) = 0.0072973... (2) = 1/(137.0360824...) (3) (Wyler 1969, 1971; OEIS A180872 and A180873), which ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

The Euler numbers, also called the secant numbers or zig numbers, are defined for |x|<pi/2 by sechx-1=-(E_1^*x^2)/(2!)+(E_2^*x^4)/(4!)-(E_3^*x^6)/(6!)+... (1) ...