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Tagged with symmetric-functions witt-vectors
5 questions
8
votes
1
answer
728
views
Criteria for ghost-Witt vectors: looking for history and references
I am looking for references (both of the readable and of the historical kind!) for the following result (which I formulate in one of its least general forms, so as not to complicate the discussion). I ...
6
votes
1
answer
348
views
Is the "renormalized third comultiplication" on $\mathbf{Symm}$ integral?
Background:
For any commutative ring $R$, let $\mathbf{Symm}_R$ be the ring of symmetric functions in countably many variables $x_1$, $x_2$, $x_3$, ... over $R$. ("Symmetric functions" really means ...
5
votes
1
answer
715
views
Are the Schur functions the minimal basis of the ring of symmetric functions with the following properties?
Let $\Lambda$ denote the ring of symmetric functions in variables $x_1,x_2,\dots$ and with coefficients in $\mathbf{Q}$. Then $\Lambda$ is freely generated as an $\mathbf{Q}$-algebra by $p_1,p_2,\dots$...
4
votes
0
answers
226
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Efficiently computing (plethysm-like?)substitutions of symmetric functions
This is a rather technical question, it arose in connection of some calculations that I need to have better grasp of the question Formal group law over $\mathbb{F}_p$ and my own older one What is ...
3
votes
0
answers
68
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Do any specializations of variables give valid equalities of series and products involving Witt symmetric functions?
Formally, Witt symmetric functions $w_n(x_1,x_2,...)$ ($n\geqslant1$) can be defined by
$$
\prod_n(1-w_nt^n)=1+\sum_k(-1)^ke_kt^k=\prod_j(1-x_jt),
$$
where $e_k(x_1,x_2,...)$ are the elementary ...