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Furthermore, we show that for general $\\lambda$, this expression factors into a symmetric and a non-symmetric part, where the symmetric part is independent of $t$, while the non-symmetric part only depends on the relative order of the entries in $\\lambda$.\n  We also examine the case $q=0$, which give rise to so called permuted-basemen"},"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":"1801.04550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-14T13:01:55Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"3d50b7bf9e0cc4e9b1f5c8cd3b2b80280aaaeda40c5a16d87e4a68621270a468","abstract_canon_sha256":"bbb8c0d060932d96a8955c0ffc49d4cb2ee3fec25a8d580da99bb9b002a89ae1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:56.437373Z","signature_b64":"DCcFA62MDROnVNB5FZGMiyVvT9mceY+pV3KWrrpvdUwTj15SYmQK6pJeHqHHcfwOVq3rxVu5RBfl6a0cARdEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e3a83858b836aaf9c398d8b8775d6691e1ba1e5903866dc140c269132b2a73","last_reissued_at":"2026-05-17T23:41:56.436685Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:56.436685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properties of non-symmetric Macdonald polynomials at $q=1$ and $q=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Mehtaab Sawhney, Per Alexandersson","submitted_at":"2018-01-14T13:01:55Z","abstract_excerpt":"We examine the non-symmetric Macdonald polynomials $E_\\lambda(x;q,t)$ at $q=1$, as well as the more general permuted-basement Macdonald polynomials. 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