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The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

An n-step Fibonacci sequence {F_k^((n))}_(k=1)^infty is defined by letting F_k^((n))=0 for k<=0, F_1^((n))=F_2^((n))=1, and other terms according to the linear recurrence ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

The Hamming graph H(d,q), sometimes also denoted q^d, is the graph Cartesian product of d copies of the complete graph K_q. H(d,q) therefore has q^d vertices. H(d,q) has ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

The Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...