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We show the following results: (1) If $d_2$ is a prime number and $\\frac{d_1}{\\gcd(d_1,d_3)}\\neq2$, then $(d_1,d_2,d_3)$ is a multidegree of a tame automorphism if and only if $d_1=d_2$ or $d_3\\in d_1\\mathbb{N}+d_2\\mathbb{N}$; (2) If $d_3$ is a prime number and $\\gcd(d_1,d_2)=1$, then $(d_1,d_2,d_3)$ is a multidegree of a tame automorphism if and only if $d_3\\in d_1\\mathbb{N}+d_2\\mathbb{N}$. We also relate this investigation with a conjecture of Drensky and Yu, which concerns with the lower bound of the degree of the Poisson bracket of two polynomia","authors_text":"Jiantao Li, Xiankun Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-04T11:58:55Z","title":"Multidegrees of Tame automorphisms with one prime number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0930","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6fc47ea17b840112ccdfb23cf3d8bac0229f68635f22635427feba8804effdf9","target":"record","created_at":"2026-05-18T03:58:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf24e6ef716b3ea879f2bc52dcede5434aabb2e7053328b91dd39dde36b2ef46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-04T11:58:55Z","title_canon_sha256":"7bf8e6512430f22aefb839a55e1ec9656fbeb747a6092e394c859d24409e4936"},"schema_version":"1.0","source":{"id":"1204.0930","kind":"arxiv","version":2}},"canonical_sha256":"74aad2fc29245aa16fa2f55ab7cda9e2c67e92d1b24c1dc29c60f074cd54f2ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74aad2fc29245aa16fa2f55ab7cda9e2c67e92d1b24c1dc29c60f074cd54f2ac","first_computed_at":"2026-05-18T03:58:24.037392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:24.037392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"soKS0LqK7lg83yLE3uNyaq6MtkoBtLFT+0XkTdzCVDx7XosIkSmYF96FKesmgOYdE2FWIy68PsMDnphoPlirAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:24.038050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fc47ea17b840112ccdfb23cf3d8bac0229f68635f22635427feba8804effdf9","sha256:6c64ae74727061055d9b9c331e40fdea3695d31174868593fa8cad97311b496c"],"state_sha256":"92ab4fa188e40cd367b221393ee738f68d77034864d7965521e6684685ad9ffd"}