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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.07604 |
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| _version_ | 1866908360474886144 |
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| author | Eisel, Roma McMullen, Valerie Muth, Robert |
| author_facet | Eisel, Roma McMullen, Valerie Muth, Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An efficient search strategy for hidden ideals in pointed partially ordered sets Eisel, Roma McMullen, Valerie Muth, Robert Combinatorics 06A07, 90C27 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. |
| title | An efficient search strategy for hidden ideals in pointed partially ordered sets |
| topic | Combinatorics 06A07, 90C27 |
| url | https://arxiv.org/abs/2505.07604 |