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The space M_L is the space spanned by all partial derivatives of \\Delta_L(X;Y). The ``shift operators'', which are particular partial symmetric derivative operators are very useful in the comprehension of the structure of the M_L spaces. We describe here how a Schur function partial derivative operator"},"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":"math/0111246","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-11-22T16:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"cbf8f8582fbe8d76fabe83dc06fa858736ab9940d451b1134e5f04d44b19cacd","abstract_canon_sha256":"7889f456ef74cdda2a9c59497480fb10b70ab7129674e909428b25d406de2499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:03.477230Z","signature_b64":"u+bP8l8yvHTOeQTFweUuOW0BrJCM+hCLezWy03/h2JqQ+SOi/D5U1Zr6GF1/HzAtUP23EPsI2I58ioxckd9UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97f5de5005c617f5254e0cee511e08ed99aed5573cae92ef07475dd092cd38e3","last_reissued_at":"2026-05-18T01:00:03.476538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:03.476538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schur Partial Derivative Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Christophe Aval, Nantel Bergeron","submitted_at":"2001-11-22T16:12:33Z","abstract_excerpt":"A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. 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