Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms for Combinatorial Systems: Well-Founded Systems and Newton
  Iterations   We consider systems of recursively defined combinatorial structures. We give
algorithms checking that these systems are well founded, computing generating
series and providing numerical values. Our framework is an articulation of the
constructible classes of Flajolet and Sedgewick with Joyal's species theory. We
extend the implicit species theorem to structures of size zero. A quadratic
iterative Newton method is shown to solve well-founded systems combinatorially.
From there, truncations of the corresponding generating series are obtained in
quasi-optimal complexity. This iteration transfers to a numerical scheme that
converges unconditionally to the values of the generating series inside their
disk of convergence. These results provide important subroutines in random
generation. Finally, the approach is extended to combinatorial differential
systems.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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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: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: econ