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product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...

A sequential substitution system is a substitution system in which a string is scanned from left to right for the first occurrence of the first rule pattern. If the pattern ...

The singleton graph is the graph consisting of a single isolated node with no edges. It is therefore the empty graph on one node. It is commonly denoted K_1 (i.e., the ...

A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane. Von Staudt (1847) classified space ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...