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Two distinct knots cannot have the same exterior. Or, equivalently, a knot is completely determined by its knot exterior (Cipra 1988; Adams 1994, p. 261). The question was ...

Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle (cf. Garnder 1986, pp. 137-138). While the ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

Let A_(k,i)(n) denote the number of partitions into n parts not congruent to 0, i, or -i (mod 2k+1). Let B_(k,i)(n) denote the number of partitions of n wherein 1. 1 appears ...

The metric of Felix Klein's model for hyperbolic geometry, g_(11) = (a^2(1-x_2^2))/((1-x_1^2-x_2^2)^2) (1) g_(12) = (a^2x_1x_2)/((1-x_1^2-x_2^2)^2) (2) g_(22) = ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

Another name for the confluent hypergeometric function of the second kind, defined by where Gamma(x) is the gamma function and _1F_1(a;b;z) is the confluent hypergeometric ...