Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking
  functions   The m-Tamari lattice of F. Bergeron is an analogue of the clasical Tamari
order defined on objects counted by Fuss-Catalan numbers, such as m-Dyck paths
or (m+1)-ary trees. On another hand, the Tamari order is related to the product
in the Loday-Ronco Hopf algebra of planar binary trees. We introduce new
combinatorial Hopf algebras based on (m+1)-ary trees, whose structure is
described by the m-Tamari lattices.
  In the same way as planar binary trees can be interpreted as sylvester
classes of permutations, we obtain (m+1)-ary trees as sylvester classes of what
we call m-permutations. These objects are no longer in bijection with
decreasing (m+1)-ary trees, and a finer congruence, called metasylvester,
allows us to build Hopf algebras based on these decreasing trees. At the
opposite, a coarser congruence, called hyposylvester, leads to Hopf algebras of
graded dimensions (m+1)^{n-1}, generalizing noncommutative symmetric functions
and quasi-symmetric functions in a natural way. Finally, the algebras of packed
words and parking functions also admit such m-analogues, and we present their
subalgebras and quotients induced by the various congruences.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex