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Descriptive Combinatorics, Computable Combinatorics, and ASI Algorithms

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arxiv 2206.08426 v1 pith:RYN57J2X submitted 2022-06-16 math.LO math.CO

Long Qian , Felix Weilacher This is my paper · ORCID
classification math.LOmath.CO
keywords combinatoricsalgorithmscomputableargumentsdescriptivekiersteadresultallows
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We introduce new types of local algorithms, which we call "ASI Algorithms", and use them to demonstrate a link between descriptive and computable combinatorics. This allows us to unify arguments from the two fields, and also sometimes to port arguments from one field to the other. As an example, we generalize a computable combinatorics result of Kierstead and use it to get within one color of the Baire measurable analogue of Vizing's Theorem. We also improve Kierstead's result for multigraphs along the way.

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Cited by 2 Pith papers

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    Any countable family of infinite subsets of a countable group admits a free flow that is minimal along each subset, with applications to disjointness and Borel complete sections.

  2. Borel Local Lemma: arbitrary random variables and limited exponential growth

    math.CO 2024-12 conditional novelty 7.0 of 10

    A Borel LLL holds for arbitrary random variables when the dependency graph exponential growth rate is bounded by a constant s satisfying a slackened LLL condition.

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