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A group action G×X->X is transitive if it possesses only a single group orbit, i.e., for every pair of elements x and y, there is a group element g such that gx=y. In this ...

Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

An n-tuple, sometimes simply called a "tuple" when the number n is known implicitly, is another word for a list, i.e., an ordered set of n elements. It can be interpreted as ...

A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

A pair of conics obtained by expanding an equation in Monge's form z=F(x,y) in a Maclaurin series z = z(0,0)+z_1x+z_2y+1/2(z_(11)x^2+2z_(12)xy+z_(22)y^2)+... (1) = ...