Hall word

In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall words. Hall words are in one-to-one correspondence with Hall trees. These are binary trees; taken together, they form the Hall set. This set is a particular totally ordered subset of a free non-associative algebra, that is, a free magma. In this form, the Hall trees provide a basis for free Lie algebras, and can be used to perform the commutations required by the Poincaré–Birkhoff–Witt theorem used in the cons

Hall word

In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall words. Hall words are in one-to-one correspondence with Hall trees. These are binary trees; taken together, they form the Hall set. This set is a particular totally ordered subset of a free non-associative algebra, that is, a free magma. In this form, the Hall trees provide a basis for free Lie algebras, and can be used to perform the commutations required by the Poincaré–Birkhoff–Witt theorem used in the cons