Tystletveyt, Morwen B.

Morvain Tistletveyt received a bachelor of arts degree from the University of Cambridge in 1967, a master's degree from the University of London in 1968 and a PhD (PhD) from the University of Manchester in 1972, where his supervisor was Michael Barat. He studied piano with Tanya Polunina, James Gibb and and gave concerts in London before deciding to devote himself to a mathematics career in 1975. He studied at to 1978 and at the from 1978 to 1987. He worked as a freelance professor at the University of California, Santa Barbara for about a year before moving to the University of Tennessee , where he is currently a professor. Thistletwate's son is also a mathematician. ^[one]

Tate's hypotheses

Morvien Tystletwaith helped prove

1. The given alternating diagrams have the minimum number of intersections .
2. Any two given alternating diagrams of a given node have the same number of twisting .
3. If any two alternating diagrams D ₁ and D _{2 of an} oriented simple alternating link D _{1 are given,} D ₁ can be transformed into D ₂ by a sequence of simple motions, called . The hypothesis is known as .
   (adapted from MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html ) ^[2]

Morvien Tystletveyt together with Louis Kaufman and K. Murasugi proved the first two Tate hypotheses in 1987. Tystletveyt and proved 1991 .

Tistletwat Algorithm

Twistlette is also famous for its Rubik's Cube Algorithm. The algorithm breaks the state of the Rubik's cube into groups that can be obtained using certain moves. These groups are:

• G ₀ = <L, R, F, B, U, D>

This group contains all the positions of the Rubik's Cube.

• G ₁ = <L, R, F, B, U2, D2>

This group contains all the positions that can be reached (from the assembled state) by rotating one-fourth of the left, right, front and back sides of the Rubik's cube, but only half-turns of the upper and lower sides.

• G ₂ = <L, R, F2, B2, U2, D2>

In this group, the states are limited to those that can be obtained by rotating the front, back, top and bottom sides of the cube one half of the left and right sides.

• G ₃ = <L2, R2, F2, B2, U2, D2>

The states of this group can be obtained only by rotating in half a turn of all faces.

• G ₄ = {I}

The final group contains only one state - the assembled cube.

The cube is assembled by moving from group to group using the moves allowed for the group. For example, a mixed cube is most likely in the G ₀ state. A table of possible permutations is viewed that use one-quarter rotations to translate a cube into a group G ₁ . Now, rotations by one quarter of the upper and lower faces are prohibited in the sequences in the table and rotations from the table are used to obtain the state G ₂ . And so on, until the cube is assembled. ^[3]

Dowker notation

Thistletwate, along with developed the , a node designation suitable for use in computers and derived from Tate and Gauss .

• Mathematics Rubik's Cube

• http://www.math.utk.edu/~morwen/ - Morwen Thistlethwaite's home page.
• Tystletveyt, Morwen B. (Eng.) In the project " Mathematical Genealogy "