{"paper":{"title":"The Whitney Duals of a Graded Poset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joshua Hallam, Rafael S. Gonz\\'alez D'Le\\'on","submitted_at":"2018-03-08T15:30:08Z","abstract_excerpt":"We introduce the notion of a \\emph{Whitney dual} of a graded poset. Two posets are Whitney duals to each other if (the absolute value of) their Whitney numbers of the first and second kind are interchanged between the two posets. We define new types of edge and chain-edge labelings which we call \\emph{Whitney labelings}. We prove that every graded poset with a Whitney labeling has a Whitney dual. Moreover, we show how to explicitly construct a Whitney dual using a technique involving quotient posets.\n  As applications of our main theorem, we show that geometric lattices, the lattice of noncros"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03151","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}