Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limiting Distributions in Generalized Zeckendorf Decompositions   An equivalent definition of the Fibonacci numbers is that they are the unique
sequence such that every integer can be written uniquely as a sum of
non-adjacent terms. We can view this as we have bins of length 1, we can take
at most one element from a bin, and if we choose an element from a bin we
cannot take one from a neighboring bin. We generalize to allowing bins of
varying length and restrictions as to how many elements may be used in a
decomposition. We derive conditions on when the resulting sequences have
uniqueness of decomposition, and (similar to the Fibonacci case) when the
number of summands converges to a Gaussian; the main tool in the proofs here is
the Lyaponuv Central Limit Theorem.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph