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The tight constant for the upper bound was recently shown to be $2$ by Cardinal, Fiorini, Joret, Jungers and Munro (STOC 2010, Combinatorica). Here, we refine this last result in case $P$ has width $2$: we show that the constant can be replaced by $2-\\varepsilon$ if one also takes into account the number of conn"},"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":"1402.5024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T15:11:13Z","cross_cats_sorted":[],"title_canon_sha256":"53f0583a1c85fb51f4e52a68931cbece4d473d96e6c83f309c6522242f6362c0","abstract_canon_sha256":"18de2d258b56bc6e5ce89b47a7aba407ab3200c4de1f6bc26ccf726895ef9ec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:14.188991Z","signature_b64":"MaF10ydZoUibgv42SREIu5lifvxZf2fg5fOgZKGLZLgH0yxRCWCY8kHk9e0rcX5qFk88/dmBZPVXPdbiJFl2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f454b64870cfd02fc8810e55270be009ead44bffd07f5eb420eacf7457412b2","last_reissued_at":"2026-05-18T02:32:14.188338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:14.188338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poset Entropy versus Number of Linear Extensions: the Width-$2$ Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Samuel Fiorini, Selim Rexhep","submitted_at":"2014-02-20T15:11:13Z","abstract_excerpt":"Kahn and Kim (J. 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