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A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

A homogeneous ideal I in a graded ring R= direct sum A_i is an ideal generated by a set of homogeneous elements, i.e., each one is contained in only one of the A_i. For ...

The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more ...

The Janko-Kharaghani graphs are two strongly regular graph on 936 and 1800 vertices. They have regular parameters (nu,k,lambda,mu)=(936,375,150,150) and (1800,1029,588,588), ...

The composition quotient groups belonging to two composition series of a finite group G are, apart from their sequence, isomorphic in pairs. In other words, if I subset H_s ...