{"paper":{"title":"Regularity of Cohen-Macaulay Specht ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kohji Yanagawa, Kosuke Shibata","submitted_at":"2020-02-06T12:21:48Z","abstract_excerpt":"For a partition $\\lambda$ of $n \\in {\\mathbb N}$, let $I^{\\rm Sp}_\\lambda$ be the ideal of $R=K[x_1,\\ldots,x_n]$ generated by all Specht polynomials of shape $\\lambda$. In the previous paper, the second author showed that if $R/I^{\\rm Sp}_\\lambda$ is Cohen-Macaulay, then $\\lambda$ is either $(n-d,1,\\ldots,1),(n-d,d)$, or $(d,d,1)$, and the converse is true if ${\\rm char}(K)=0$. In this paper, we compute the Hilbert series of $R/I^{\\rm Sp}_\\lambda$ for $\\lambda=(n-d,d)$ or $(d,d,1)$. Hence, we get the Castelnuovo-Mumford regularity of $R/I^{\\rm Sp}_\\lambda$, when it is Cohen-Macaulay. In partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02221","kind":"arxiv","version":4},"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/2002.02221/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"}