Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A noncommutative cycle index and new bases of quasi-symmetric functions
  and noncommutative symmetric functions   We define a new basis of the algebra of quasi-symmetric functions by lifting
the cycle-index polynomials of symmetric groups to noncommutative polynomials
with coefficients in the algebra of free quasi-symmetric functions, and then
projecting the coefficients to $QSym$. By duality, we obtain a basis of
noncommutative symmetric functions, for which a product formula and a
recurrence in the form of a combinatorial complex are obtained. This basis
allows to identify noncommutative symmetric functions with the quotient of
FQSym induced by the pattern-replacement relation $321 \equiv 231$ and $312
\equiv 132$.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th