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Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Given a sample of n variates X_1, ..., X_N, reorder them so that Y_1<Y_2<...<Y_N. Then Y_i is called the ith order statistic (Hogg and Craig 1970, p. 146), sometimes also ...

Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

A plaindrome is a number whose hexadecimal digits are in nondecreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, ...

The quaternion group is one of the two non-Abelian groups of the five total finite groups of order 8. It is formed by the quaternions +/-1, +/-i, +/-j, and +/-k , denoted Q_8 ...

The Robertson graph is the unique (4,5)-cage graph, illustrated above. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic ...

Scientific notation is the expression of a number n in the form a×10^p, where p=|_log_(10)|n|_| (1) is the floor of the base-10 logarithm of n (the "order of magnitude"), and ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...