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Denote by $\\mathcal C(o, n)$ (resp. $\\mathcal C'(o, n)$) the set of (resp. primitive) conjugacy classes of pointed length at most $n$ for a basepoint $o$. The main result is an asymptotic formula as follows: $$\\sharp \\mathcal C(o, n) \\asymp \\sharp \\mathcal C'(o, n) \\asymp \\frac{\\exp(\\omega(G)n)}{n}.$$ A similar formula holds for conjugacy classes using stable length. As a consequence of the formulae, the conjugacy growth "},"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":"1810.02969","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-10-06T09:46:26Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"0492e3c4473240b5cbce21bbdf13a859f4ad4deb85bcfb0a46f606711d4d5e50","abstract_canon_sha256":"5f3cb5d758806255294652e232f38791a831c24dc0b225a0abea143a7622f106"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:22.580925Z","signature_b64":"zqDv3GeAzt6pD3Fvi9OXLae54GAM3cOFMF+dKxEc3bNQl+eAK2Soytq2JOcdqvrdXj/xxjGWKdPi1ZWH5nFtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3b3ba522a99a7c2972e9770474a442ffaf08bca08bf80c64a2390f635c0ace7","last_reissued_at":"2026-07-05T03:57:22.580483Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:22.580483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting conjugacy classes in groups with contracting elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Gekhtman, Wen-yuan Yang","submitted_at":"2018-10-06T09:46:26Z","abstract_excerpt":"In this paper, we derive an asymptotic formula for the number of conjugacy classes of elements in a class of statistically convex-cocompact actions with contracting elements. Denote by $\\mathcal C(o, n)$ (resp. $\\mathcal C'(o, n)$) the set of (resp. primitive) conjugacy classes of pointed length at most $n$ for a basepoint $o$. The main result is an asymptotic formula as follows: $$\\sharp \\mathcal C(o, n) \\asymp \\sharp \\mathcal C'(o, n) \\asymp \\frac{\\exp(\\omega(G)n)}{n}.$$ A similar formula holds for conjugacy classes using stable length. 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