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arXiv · 2505.07604

An efficient search strategy for hidden ideals in pointed partially ordered sets

Roma Eisel·Valerie McMullen·Robert Muth
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Abstract

We consider a combinatorial question about searching for an unknown ideal $μ$ within a known pointed poset $λ$. Elements of $λ$ may be queried for membership in $μ$, but at most $k$ positive queries are permitted. We provide a general search strategy for this problem, and establish new bounds (based on $k$ and the degree and height of $λ$) for the total number of queries required to identify $μ$. We show that this strategy performs asymptotically optimally on the family of complete $\ell$-ary trees as the height grows.

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Roma Eisel, Valerie McMullen, Robert Muth. 2025-05-12. An efficient search strategy for hidden ideals in pointed partially ordered sets. https://arxiv.org/abs/2505.07604

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