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A ring torus constructed out of a square of side length c can be dissected into two squares of arbitrary side lengths a and b (as long as they are consistent with the size of ...

The function defined by y_+^alpha={y^alpha for y>0; 0 for y<=0. (1)

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

A union-closed set is a nonempty finite collection of distinct nonempty finite sets which is closed under union.

Young's lattice Y_p is the partial order of partitions contained within a partition p ordered by containment (Stanton and White 1986; Skiena 1990, p. 77).

A k-partite graph is a graph whose graph vertices can be partitioned into k disjoint sets so that no two vertices within the same set are adjacent.

A p-elementary subgroup of a finite group G is a subgroup H which is the group direct product H=C_n×P, where P is a p-group, C_n is a cyclic group, and p does not divide n.

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

An infinite sequence of positive integers a_i satisfying 1<=a_1<a_2<a_3<... (1) is an A-sequence if no a_k is the sum of two or more distinct earlier terms (Guy 1994). Such ...

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...