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arXiv · 2009.07348

Searching for quicksand ideals in partially ordered sets

Alexas Iams·Hannah Johnston·Robert Muth
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Abstract

We consider a combinatorial question about searching for an unknown ideal $μ$ within a known poset $λ$. Elements of $λ$ may be queried for membership in $μ$, but at most $k$ positive query results are permitted. The goal is to find a search strategy which guarantees a solution in a minimal total number $m_k(λ)$ of queries. We provide tight bounds for $m_k(λ)$, and construct optimal search strategies for the case where $k=2$ and $λ$ is the product poset of totally ordered finite sets, one of which has cardinality not more than six.

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Alexas Iams, Hannah Johnston, Robert Muth. 2020-09-15. Searching for quicksand ideals in partially ordered sets. https://arxiv.org/abs/2009.07348

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