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A proving technique in homological algebra which consists in looking for equivalent map compositions in commutative diagrams, and in exploiting the properties of injective, ...

Any lemma on commutative diagrams. It can give relations between maps (as in the five lemma) or tell how to construct new diagrams from old ones (as in the snake lemma).

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

The diamond graph is the simple graph on 4 nodes and 5 edges illustrated above (Brandstädt et al. 1987, p. 18). It is isomorphic to the complete tripartite graph K_(1,1,2) ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...

Two manifolds are said to be diffeomorphic if there exists a diffeomorphism between them.