Questions tagged [plethory]

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11 votes
1 answer
611 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 ...
darij grinberg's user avatar
6 votes
2 answers
588 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). ...
Martin Brandenburg's user avatar
5 votes
1 answer
430 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 ...
Jacques Carette's user avatar