{"paper":{"title":"Tame Decompositions and Collisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Konstantin Ziegler","submitted_at":"2014-02-24T20:57:07Z","abstract_excerpt":"A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The tame case, where the characteristic p of Fq does not divide n = deg f, is fairly well-understood, and we have reasonable bounds on the number of decomposables of degree n. Nevertheless, no exact formula is known if $n$ has more than two prime factors. In order to count the decomposables, one wants to know, under a suitable normalization, the number of collision"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5945","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}