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Gessel, Matthias Beck, Sunyoung Lee","submitted_at":"2009-06-30T16:14:29Z","abstract_excerpt":"Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \\geq 1$, a symmetrically constrained composition $\\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints\n  ${\\sum_{i=1}^n a_i \\lambda_{\\pi(i)} \\geq 0 : \\pi \\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration."},"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":"0906.5573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-06-30T16:14:29Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a21d2bc2bb905d201e7ec623b4c2386f9c432159a0deefb664ed53f54ff27663","abstract_canon_sha256":"b5da6260394ffe8c503b2ab464ff3d8f6aa76b9fd7a75f74e55a091fb44607bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:53.050116Z","signature_b64":"yV7PPuzygXNgi+751NoTpftyA9W7UDA4SC+FmdZgKuA/N35du8874fENWZGmdqQSqn3oFrxGJhPgev6+XkisAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"614dfd740402e867d97ed93ac4a8fe2dd6b5659ff4dd5458d0421240e0600f6a","last_reissued_at":"2026-05-18T03:07:53.049573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:53.049573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetrically Constrained Compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Carla D. 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