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A problem in the theory of algebraic invariants that was solved by Hilbert using an existence proof.

A metric characterizing the difference between two knots K and K^' in S^3.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

The index set for the collection of submodules in a graded module.

A graph cycle.

The multiplicity of a multigraph is its maximum edge multiplicity.

A section of a graph obtained by finding its intersection with a plane.

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

A gyrobicupola is a bicupola in which the bases are in opposite orientations.

A birotunda in which the bases are in opposite orientations.