{"paper":{"title":"Intersection matrices revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CO","authors_text":"E. Ghorbani, M. Mohammad-Noori, N. Ghareghani","submitted_at":"2009-02-25T13:21:01Z","abstract_excerpt":"Several intersection matrices of $s$-subsets vs. $k$-subsets of a $v$-set are introduced in the literature. We study these matrices systematically through counting arguments and generating function techniques. A number of new or known identities appear as natural consequences of this viewpoint; especially, appearance of the derivative operator $d/dz$ and some related operators reveals some connections between intersection matrices and the \"combinatorics of creation-annihilation\". As application, the eigenvalues of several intersection matrices including some generalizations of the adjacency ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4367","kind":"arxiv","version":4},"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"}