{"paper":{"title":"Khovanskii bases of subalgebras arising from finite distributive lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani, Koichiro Tani, Koji Matsushita","submitted_at":"2025-01-10T05:38:29Z","abstract_excerpt":"The notion of Khovanskii bases was introduced by Kaveh and Manon. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was introduced by Robbiano and Sweedler as an analogue of Gr\\\"{o}bner bases in the context of subalgebras. A Hibi ideal is an ideal of a polynomial ring that arises from a distributive lattice. For the development of an analogy of the theory of Hibi ideals and Gr\\\"{o}bner bases within the framework of subalgebras, in this paper, we investigate when the set of the polynomials associated with a distributive lattice forms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05720","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.05720/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}