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The thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

The lower matching number of a graph is the minimum size of a maximal independent edge set. The (upper) matching number may be similarly defined as the largest size of an ...

A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...

Every position of every impartial game has a nim-value, making it equivalent to a nim-heap. To find the nim-value (also called the Sprague-Grundy number), take the mex of the ...

An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases.

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

For a finite group G, let p(G) be the subgroup generated by all the Sylow p-subgroups of G. If X is a projective curve in characteristic p>0, and if x_0, ..., x_t are points ...