Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular Catalan Numbers   The Catalan number $C_n$ enumerates parenthesizations of $x_0*\dotsb*x_n$
where $*$ is a binary operation. We introduce the modular Catalan number
$C_{k,n}$ to count equivalence classes of parenthesizations of $x_0*\dotsb*x_n$
when $*$ satisfies a $k$-associative law generalizing the usual associativity.
This leads to a study of restricted families of Catalan objects enumerated by
$C_{k,n}$ with emphasis on binary trees, plane trees, and Dyck paths, each
avoiding certain patterns. We give closed formulas for $C_{k,n}$ with two
different proofs. For each $n\ge0$ we compute the largest size of
$k$-associative equivalence classes and show that the number of classes with
this size is a Catalan number.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph