: Mathematics: quasisymmetric function

mathematical analysis > function > symmetric function > quasisymmetric function

mathematical analysis > combinatorics > algebraic combinatorics > quasisymmetric function

algebra > combinatorics > algebraic combinatorics > quasisymmetric function

algebra > representation theory > Hopf algebra > quasisymmetric function

... > abstract algebra > algebraic structure > associative algebra > Hopf algebra > quasisymmetric function

category theory > Hopf algebra > quasisymmetric function

... > abstract algebra > algebraic structure > bialgebra > Hopf algebra > quasisymmetric function

quasisymmetric function

In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in n variables, as n goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number n of variables (but its elements are neither polynomials nor functions).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Quasisymmetric_function)

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