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Define the positive Eulerian polynomial $A_n^+(t)$ as the polynomial obtained when we sum descents over the alternating group. We show that $A_n^+(t)$ is gamma positive iff $n \\equiv 0,1$ (mod 4). When $n \\equiv 2$ (mod 4) we show that $A_n^+(t)$ can be written as a sum of two gamma positive polynomials while if $n \\equiv 3$ (mod 4), we show that $A_n^+(t)$ can be written as a sum of three gamma positive polynomials.\n  Similar results are shown when we consider the positive type-D and type-D Eulerian polynomials.","authors_text":"Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-05T11:49:16Z","title":"Gamma positivity of the Descent based Eulerian polynomial in positive elements of Classical Weyl Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01927","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c82e548392358df1a47e9e4fc582e5f2150f81e68a5e7b5490fcf5a96e9ce5b4","target":"record","created_at":"2026-05-17T23:59:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ef4d0ef393b8d616dc6a26160144490d1b8b8ee6f4dcdc3fdd9ef21e8c60654","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-05T11:49:16Z","title_canon_sha256":"75f595128832f4b9235729cbaf534a517c22e3ec87765af1efb117e8d4a343b7"},"schema_version":"1.0","source":{"id":"1812.01927","kind":"arxiv","version":1}},"canonical_sha256":"15192cd3874333a2441a7a70ff49147aaaf07cc1eecea2764c35bc20a63b1a49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15192cd3874333a2441a7a70ff49147aaaf07cc1eecea2764c35bc20a63b1a49","first_computed_at":"2026-05-17T23:59:00.221764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:00.221764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cvCx+u7adycUH2SPBXbWj3SCcW7KYVj5m2kScEsFPlgCmR0D38/AlpR1l4J5+IZheh4t4/saYWdd7nyHb+AkDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:00.222197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c82e548392358df1a47e9e4fc582e5f2150f81e68a5e7b5490fcf5a96e9ce5b4","sha256:322677f8e0d2d49b53b9d505f955fe3642821def82d98bb80982df836df26ec8"],"state_sha256":"947ce026649017883cae40156f50da94496fb618a9a28afb1d3018961bbe3eb2"}