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We describe reversible maps in certain groups of interval exchange transformations namely $G_n \\simeq (\\mathbb S^1)^n \\rtimes\\mathcal S_n $, where $\\mathbb S^1$ is the circle and $\\mathcal S_n $ is the group of permutations of $\\{1,...,n\\}$. We first characterize strongly reversible maps, then we show that reversible elements are strongly reversible. As a corollary, we obtain that composites of involutions in $G_n$ are product "},"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":"1907.01808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-03T09:23:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4c0b1d8f6a7be455b7f393aedda7c6de61e3a09fa59606ad9fbdefba8197226e","abstract_canon_sha256":"7bd0433b0d1e652e37546c53a3b289a863f944d882185811e5b6ac88d2ea67d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.968630Z","signature_b64":"/uqkDWXGSRyZb0CIfVO6eBFjmqpHx4xmip0qviupSXdPu8QDERz6iJloNAm5gb+Wkc155qeDjIQbHXuYhuvmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e758007ef2fedc6f7a9c757419969af60cd0394989d641ad9066db1071ea68e0","last_reissued_at":"2026-05-17T23:41:34.967937Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.967937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reversible Maps and Products of Involutions in Groups of IETS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Isabelle Liousse (LPP), Nancy Guelman","submitted_at":"2019-07-03T09:23:39Z","abstract_excerpt":"An element $f$ of a group $G$ is reversible if it is conjugated in $G$ to its own inverse; when the conjugating map is an involution, $f$ is called strongly reversible. We describe reversible maps in certain groups of interval exchange transformations namely $G_n \\simeq (\\mathbb S^1)^n \\rtimes\\mathcal S_n $, where $\\mathbb S^1$ is the circle and $\\mathcal S_n $ is the group of permutations of $\\{1,...,n\\}$. We first characterize strongly reversible maps, then we show that reversible elements are strongly reversible. 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