Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polygonal Dissections and Reversions of Series   The Catalan numbers $C_k$ were first studied by Euler, in the context of
enumerating triangulations of polygons $P_{k+2}$. Among the many
generalizations of this sequence, the Fuss-Catalan numbers $C^{(d)}_k$ count
enumerations of dissections of polygons $P_{k(d-1)+2}$ into $(d+1)$-gons. In
this paper, we provide a formula enumerating polygonal dissections of
$(n+2)$-gons, classified by partitions $\lambda$ of $[n]$. We connect these
counts $a_{\lambda}$ to reverse series arising from iterated polynomials.
Generalizing this further, we show that the coefficients of the reverse series
of polynomials $x=z-\sum_{j=0}^{\infty} b_j z^{j+1}$ enumerate colored
polygonal dissections.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs