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Given a set of permutations $\\Pi$, let $\\mathfrak{S}_n(\\Pi)$ denote the set of permutations in the symmetric group $\\mathfrak{S}_n$ that avoid every element of $\\Pi$ in the sense of pattern avoidance. For each set $\\Pi$ appearing in their conjecture, we show that the pairs of statistics $(\\mathrm{des},\\mathrm{fix})$ and $(\\mathrm{ides},\\mathrm{pix})$ are equidistributed over $\\mathfrak{S}"},"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":"2606.00646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T09:46:06Z","cross_cats_sorted":[],"title_canon_sha256":"002c942129ef3a59558352dc75986e0c19c45f8f5c07ce04d228e4b1f22b55e1","abstract_canon_sha256":"417a1d32cf1c6ab589e09aec1d241c0a59fb3165758b489109d97aa865178f58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:00.817251Z","signature_b64":"g3Tt3/CYMdpdBqsFSVrrymzu98E0u+zPYr78tXVF3967s8CxYOrx/2oW2PmLL/55HhL5buDInzsPvz+YHB5xDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97094f742bcc9fc338fae622a3cb0b9db1e7374502bd572c04dc7fd080f131f4","last_reissued_at":"2026-06-02T01:04:00.816541Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:00.816541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Refinement of the Fixed--Pixed Points Equidistribution on restricted Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chao Xu, Yao Dong","submitted_at":"2026-05-30T09:46:06Z","abstract_excerpt":"Motivated by a recent conjecture of Bsila, Cox, Hugo, Styron and Zhuang concerning fixed points and pixed points on pattern-avoiding permutations, we prove a bivariate refinement involving descent statistics. 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