Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern groups and a poset based Hopf monoid   The supercharacter theory of algebra groups gave us a representation
theoretic realization of the Hopf algebra of symmetric functions in
noncommuting variables. The underlying representation theoretic framework comes
equipped with two canonical bases, one of which was completely new in terms of
symmetric functions. This paper simultaneously generalizes this Hopf structure
by considering a larger class of groups while also restricting the
representation theory to a more combinatorially tractable one. Using the normal
lattice supercharacter theory of pattern groups, we not only gain a third
canonical basis, but also are able to compute numerous structure constants in
the corresponding Hopf monoid, including coproducts and antipodes for the new
bases.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph