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A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...

A numerical knot invariant. For a tame knot K, the bridge index is the least bridge number of all planar representations of the knot. The bridge index of the unknot is ...

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

Chinese checkers is a game roughly analogous to checkers played on a board in the shape of a centered hexagram. The board has a total of S_5=121 holes, where S_n is a star ...

The set P^2 is the set of all equivalence classes [a,b,c] of ordered triples (a,b,c) in C^3\(0,0,0) under the equivalence relation (a,b,c)∼(a^',b^',c^') if ...

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

Consider a set of points X_i on an attractor, then the correlation integral is C(l)=lim_(N->infty)1/(N^2)f, where f is the number of pairs (i,j) whose distance |X_i-X_j|<l. ...