Questions tagged [plethory]

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9
votes
1answer
523 views

Plethysm of $\mathrm{QSym}$ into $\mathrm{QSym}$: can it be defined?

I will denote by $\Lambda$ the ring of symmetric functions, and by $\mathrm{QSym}$ the ring of quasisymmetric functions (both in infinitely many variables $x_1$, $x_2$, $x_3$, ..., both over $\mathbb ...
5
votes
1answer
331 views

Are plethories a theory of basis-free polynomials?

This question is a follow-up to a question about the theory of polynomials. It should be quite clear by now that matrix theory and linear algebra are quite different topics. As the various answers ...
4
votes
2answers
494 views

Classification of plethories over $\mathbb{Q}$

Let $k$ be a commutative ring. For every cocommutative bialgebra $A$ over $k$ the symmetric algebra of the underlying $k$-module $S(A)$ carries the structure of a $k$-plethory (Borger, Wieland, 2.5). ...