"Gray code" of all permutations
From V. L. Kompel'makher and V. A. Liskovets, "Sequential generation of arrangements by means of a basis of transpositions", Kibernetika 3, 17, May-June, 1975:
It is well known ([1], p. 28) that all $n!$ arrangements of $n$ symbols can be ordered without repetition so that each can be obtained from the previous one by a single transposition.
See also C. Savage, "A survey of combinatorial Gray codes", SIAM Rev., 39, 605 (1997):
Examples of combinatorial Gray codes include (1) listing all permutations of $1 \dots n$ so that consecutive permutations differ only by the swap of one pair of adjacent elements [Joh63, Tro62]
This is also addressed in Example 7.3.1 in Joyner's Adventures in Group Theory.
In Knuth's second fascicle of volume 4 of The Art of Computer Programming, he gives "algorithm P" (or more colloquially, the method of plain changes) for generating the permutations of a sequence with distinct elements by repeatedly interchanging adjacent pairs.
Earlier in the book, however, Knuth gives a cold shower on the possibility of doing something similar for multisets with repeated elements. He gives the following example, which does not have a Hamiltonian path:
