Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hopf algebra of finite topologies and T-partitions   A noncommutative and noncocommutative Hopf algebra on finite topologies H_T
is introduced and studied (freeness, cofreeness, self-duality...). Generalizing
Stanley's definition of P-partitions associated to a special poset, we define
the notion of T-partitions associated to a finite topology, and deduce a Hopf
algebra morphism from H_T to the Hopf algebra of packed words WQSym.
Generalizing Stanley's decomposition by linear extensions, we deduce a
factorization of this morphism, which induces a combinatorial isomorphism from
the shuffle product to the quasi-shuffle product of WQSym. It is strongly
related to a partial order on packed words, here described and studied.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin