Searching for quicksand ideals in partially ordered sets
Abstract
We consider a combinatorial question about searching for an unknown ideal $\mu$ within a known poset $\lambda$. Elements of $\lambda$ may be queried for membership in $\mu$, 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 $m_k(\lambda)$ of queries. We provide tight bounds for $m_k(\lambda)$, and construct optimal search strategies for the case where $k=2$ and $\lambda$ is the product poset of totally ordered finite sets, one of which has cardinality not more than six.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.07348
- arXiv:
- arXiv:2009.07348
- Bibcode:
- 2020arXiv200907348I
- Keywords:
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- Mathematics - Combinatorics