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However, it turns out that the expectation of $L_n M_n -L_n$ grows as fast as $\\frac{1}{2}\\log{n}$ We obtain a precise asymptotic expansion for this expectation and conclude with an open problem arising fr"},"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":"1712.03233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-08T15:22:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5a67f3bf55640b488c59cf4e20b445dbf4fc1794cf7984064398f768147b1be4","abstract_canon_sha256":"c538e0b0da2459d0ee6b47931165a7f48c85bb9ec94663130f1256f1923dff8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:21.919440Z","signature_b64":"rTc7Sf2ALUhUlqvIHVpvQdLBrudcChJfFMHkpNnqRZWfHRddM5YVMAnkLO+uSPNHWeRYakGJAndG0NwmR+eMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4e9eafc3b7722b7fc912a344404bf566d4cee4c094bcd73d1ccb2c4aac7faef","last_reissued_at":"2026-05-18T00:28:21.918828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:21.918828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Largest Part Size and Its Multiplicity of a Random Integer Partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2017-12-08T15:22:06Z","abstract_excerpt":"Let $\\lambda$ be a partition of the positive integer $n$ chosen umiformly at random among all such partitions. 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