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Also for a large class of free resolutions F., encompassing Eliahou-Kervaire resolutions, we show that a Gr\\\"obner basis for Z_p is given by the boundaries of generators of F_p. We apply the above to give lower bounds for the Stanley depth of the syzygy modules Z_p, in particular showing it is at least p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1003.4495","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-23T19:23:05Z","cross_cats_sorted":[],"title_canon_sha256":"59eef5b803c7561968e037e2bad4dbcb20cd2432eb3fbf250125233b5cb3031a","abstract_canon_sha256":"005312590906565217752ffb890b8977c3529bf6ec7643c1bbe48a1cbb7b17ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:41.282444Z","signature_b64":"BIilVD7hfg+YJemg5uvqKs2AwnIAEvDvQOqcmMcrt/KNRfncAqUTXeceOYzNMfVzHREugElwmz0qHpB9w46iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60daa353de05183fb73a544d17ea97b2c4a7225471d30376c57679d97f047f41","last_reissued_at":"2026-05-18T01:03:41.281890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:41.281890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gr\\\"obner bases of syzygies and Stanley depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Gunnar Floystad, Juergen Herzog","submitted_at":"2010-03-23T19:23:05Z","abstract_excerpt":"Let F. be a any free resolution of a Z^n-graded submodule of a free module over the polynomial ring K[x_1, ..., x_n]. 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