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Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are ...

Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

A canonical labeling, also called a canonical form, of a graph G is a graph G^' which is isomorphic to G and which represents the whole isomorphism class of G (Piperno 2011). ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

A complemented lattice is an algebraic structure (L, ^ , v ,0,1,^') such that (L, ^ , v ,0,1) is a bounded lattice and for each element x in L, the element x^' in L is a ...

A table made by subtracting adjacent entries in a sequence, then repeating the process with those numbers.

A structure consisting of an ordered set of sorted lists such that the head and tail entries of later lists nest within earlier ones. For example, an encroaching list set for ...