{"paper":{"title":"Combinatorics of poly-Bernoulli numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Be\\'ata B\\'enyi, Peter Hajnal","submitted_at":"2015-10-20T06:02:14Z","abstract_excerpt":"The ${\\mathbb B}_n^{(k)}$ poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers ($B_n={\\mathbb B}_n^{(1)}$) --- were introduced by Kaneko in 1997. When the parameter $k$ is negative then ${\\mathbb B}_n^{(k)}$ is a nonnegative number. Brewbaker was the first to give combinatorial interpretation of these numbers. He proved that ${\\mathbb B}_n^{(-k)}$ counts the so called lonesum $0\\text{-}1$ matrices of size $n\\times k$. Several other interpretations were pointed out. We survey these and give new ones. Our new interpretation, for example, gives a transparent, combina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05765","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"}