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An unknot which can only be unknotted by first increasing the number of crossings.

mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.

Approximates the possible values of y in terms of x if sum_(i,j=0)^na_(ij)x^iy^j=0.

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

An algebraic surface of degree 9. Enneper's minimal surface is an example of a nonic surface.

In the American system, 10^(30).

A quantity which is either 0 (zero) or positive, i.e., >=0.

A quantity that is nonzero everywhere is said to be nonvanishing. For instance, the values of x^2+1 are nonvanishing for real x, while those of x^2 are not (since x^2 ...