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We say that a deformation is $W$-equivariant if the number of parallel hyperplanes of each hyperplane $H\\in \\A$ depends only on the $W$-orbit of $H$. We prove that the conings of the $W$-equivariant deformations are free arrangements under a Shi-Catalan condition and give a formula for the number of chambers."},"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":"1012.5884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-29T08:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"691e82ca46f469cc268a71484d0d0b194b527ec2e619a55fa3068066ccfbad58","abstract_canon_sha256":"28273be30928b33f1a96130606bb55b8b466b34f957ebc93caab41d6dfb17f49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:55.218549Z","signature_b64":"VdfSmxw40DOiR7bL/qBGMeNrPNzQth/d9Nt8aRcVtkavkUthviQtRWqvbEYu0rCY/tJtm/kEoFBZWyfayhTTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb80d504a9955f33412b4129d644b4b00396d54fcec8654e275399e91578893e","last_reissued_at":"2026-05-18T04:13:55.218000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:55.218000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The freeness of Shi-Catalan arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroaki Terao, Takuro Abe","submitted_at":"2010-12-29T08:10:14Z","abstract_excerpt":"Let $W$ be a finite Weyl group and $\\A$ be the corresponding Weyl arrangement. 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