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We show that there exists a function $G(n)$ such that the partitions of $n$ can be reconstructed from their multisets of $k$-minors if and only if $"},"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":"1610.05354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-17T20:54:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"91c21110348dd42bb461c32a32a0e708f475f759eb95844c2114d75b3a7d742a","abstract_canon_sha256":"9d0e6834a16b686b4dfe6fa6bd34514e7ec02f0e9bcb66a80ff842f24d0a5b1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:59.564509Z","signature_b64":"k5gYGwm9YYOzF7P4dYrdPmg1rHXHA5cvJNrI+C240fQP6LxeVMcSWMHJ6OHEHvfJFq3FCCAFgJRMNlx9OsQiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b19925d6f9120d49bc36a7c18f069ec27f41a4195763686b0d08bf1172628e2","last_reissued_at":"2026-05-18T01:01:59.563994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:59.563994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstructing Partitions from their Multisets of $k$-Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Pakawut Jiradilok","submitted_at":"2016-10-17T20:54:20Z","abstract_excerpt":"For non-negative integers $n$ and $k$ with $n \\ge k$, a {\\em $k$-minor} of a partition $\\lambda = [\\lambda_1, \\lambda_2, \\dots]$ of $n$ is a partition $\\mu = [\\mu_1, \\mu_2, \\dots]$ of $n-k$ such that $\\mu_i \\le \\lambda_i$ for all $i$. 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