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We show that $|\\mathcal{A}_{\\boldsymbol\\lambda}|= \\mathcal{T}(\\boldsymbol\\lambda)\\,q^{r-m}+\\mathcal{O}(q^{r-m-{1}/{2}})$, where $\\mathcal{T}(\\boldsymbol\\lambda)$ is the proportion of elements of the symmetric group of $r$ elements with cycle pattern $\\boldsymbol\\lambda$ and $m$ is the codimension of $\\mathcal{A}$. We provide explicit u"},"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":"1807.08052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-20T23:09:18Z","cross_cats_sorted":[],"title_canon_sha256":"0236d3b9f38bdc4c6ec63b87a9dc2f751e6e858ce4021c0840ff6dc3635f4dcc","abstract_canon_sha256":"ece738d53ec53d156fa4451b8d540080037e90da484a6d3c31d17c82c222800d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:09.468683Z","signature_b64":"hzzk2DZ8r/C+ZKn30iWwxlNJPNGddKns9zbSmZOBSdWa6nGPvmG3Io1wBvN25JdGD/sdXIhiBixCYUqszsEwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ffe756e8be1bdf2aa3c547c124e160a24de56c2239e3980557d3dc13e11ea78","last_reissued_at":"2026-05-18T00:10:09.468035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:09.468035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorization patterns on nonlinear families of univariate polynomials over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2018-07-20T23:09:18Z","abstract_excerpt":"We estimate the number $|\\mathcal{A}_{\\boldsymbol\\lambda}|$ of elements on a nonlinear family $\\mathcal{A}$ of monic polynomials of $\\mathbb{F}_q[T]$ of degree $r$ having factorization pattern $\\boldsymbol\\lambda:=1^{\\lambda_1}2^{\\lambda_2}\\cdots r^{\\lambda_r}$. We show that $|\\mathcal{A}_{\\boldsymbol\\lambda}|= \\mathcal{T}(\\boldsymbol\\lambda)\\,q^{r-m}+\\mathcal{O}(q^{r-m-{1}/{2}})$, where $\\mathcal{T}(\\boldsymbol\\lambda)$ is the proportion of elements of the symmetric group of $r$ elements with cycle pattern $\\boldsymbol\\lambda$ and $m$ is the codimension of $\\mathcal{A}$. 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