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Forbidden Hypermatrices Imply General Bounds on Induced Forbidden Subposet Problems


We prove that for every poset P, there is a constant CP such that the size of any family of subsets of {1, 2, . . ., n} that does not contain P as an induced subposet is at most $$C_P{\binom{n}{\lfloor\gfrac{n}{2}\rfloor}},$$ settling a conjecture of Katona, and Lu and Milans. We obtain this bound by establishing a connection to the theory of forbidden submatrices and then applying a higher-dimensional variant of the Marcus–Tardos theorem, proved by Klazar and Marcus. We also give a new proof of their result.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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