Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generation, Ranking and Unranking of Ordered Trees with Degree Bounds   We study the problem of generating, ranking and unranking of unlabeled
ordered trees whose nodes have maximum degree of $\Delta$. This class of trees
represents a generalization of chemical trees. A chemical tree is an unlabeled
tree in which no node has degree greater than 4. By allowing up to $\Delta$
children for each node of chemical tree instead of 4, we will have a
generalization of chemical trees. Here, we introduce a new encoding over an
alphabet of size 4 for representing unlabeled ordered trees with maximum degree
of $\Delta$. We use this encoding for generating these trees in A-order with
constant average time and O(n) worst case time. Due to the given encoding, with
a precomputation of size and time O(n^2) (assuming $\Delta$ is constant), both
ranking and unranking algorithms are also designed taking O(n) and O(nlogn)
time complexities.

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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess