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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"},"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":"1204.0930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-04T11:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"7bf8e6512430f22aefb839a55e1ec9656fbeb747a6092e394c859d24409e4936","abstract_canon_sha256":"bf24e6ef716b3ea879f2bc52dcede5434aabb2e7053328b91dd39dde36b2ef46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:24.038050Z","signature_b64":"soKS0LqK7lg83yLE3uNyaq6MtkoBtLFT+0XkTdzCVDx7XosIkSmYF96FKesmgOYdE2FWIy68PsMDnphoPlirAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74aad2fc29245aa16fa2f55ab7cda9e2c67e92d1b24c1dc29c60f074cd54f2ac","last_reissued_at":"2026-05-18T03:58:24.037392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:24.037392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multidegrees of Tame automorphisms with one prime number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jiantao Li, Xiankun Du","submitted_at":"2012-04-04T11:58:55Z","abstract_excerpt":"Let $3\\leq d_1\\leq d_2\\leq d_3$ be integers. 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 $d_3\\in d_1\\mathbb{N}+d_2\\mathbb{N}$. 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