Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distribution of variables in lambda-terms with restrictions on De Bruijn
  indices and De Bruijn levels   We investigate the number of variables in two special subclasses of
lambda-terms that are restricted by a bound of the number of abstractions
between a variable and its binding lambda, the so-called De-Bruijn index, or by
a bound of the nesting levels of abstractions, \textit{i.e.}, the number of De
Bruijn levels, respectively. These restrictions are on the one hand very
natural from a practical point of view, and on the other hand they simplify the
counting problem compared to that of unrestricted lambda-terms in such a way
that the common methods of analytic combinatorics are applicable.
  We will show that the total number of variables is asymptotically normally
distributed for both subclasses of lambda-terms with mean and variance
asymptotically equal to $Cn$ and $\tilde{C}n$, respectively, where the
constants $C$ and $\tilde{C}$ depend on the bound that has been imposed. So far
we just derived closed formulas for the constants in case of the class of
lambda-terms with bounded De Bruijn index. However, for the other class of
lambda-terms that we consider, namely lambda-terms with a bounded number of De
Bruijn levels, we investigate the number of variables, as well as abstractions
and applications, in the different De Bruijn levels and thereby exhibit a
so-called "unary profile" that attains a very interesting shape.

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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas