QSymM

The monomial basis of the quasi-symmetric functions, indexed by a composition. The product is the quasi-shuffle, which may ADD two leading parts as well as interleave them.

WikipediaQuasisymmetric function↗WikidataQ7269535↗

QSymM([1,2]) for the composition

NSymH([1,2])the complete basis of NSym, whose product is concatenation

Domain: Hopf algebras

Details

• — the term is the overlap, and it is what makes this a QUASI-shuffle rather than an ordinary shuffle
• QSym is commutative; NSym is not, which is what its name records
• Both are graded with basis elements in degree — one per composition of
• The two share an index set but are different algebras: mixing and in one product is refused
• Use the ordered product (NonCommutativeMultiply or ); see Coproduct for the other half of the structure

Examples

See also: Coproduct, Antipode, Basis