{"paper":{"title":"A sign-reversing involution for an extension of Torelli's Pfaffian identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"N. Bradley Fox, Richard Ehrenborg","submitted_at":"2014-08-27T13:24:09Z","abstract_excerpt":"We evaluate the hyperpfaffian of a skew-symmetric $k$-ary polynomial $f$ of degree $k/2 \\cdot (n-1)$. The result is a product of the Vandermonde product and a certain expression involving the coefficients of the polynomial $f$. The proof utilizes a sign reversing involution on a set of weighted, oriented partitions. When restricting to the classical case when $k=2$ and the polynomial is $(x_{j} - x_{i})^{n-1}$, we obtain an identity due to Torelli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6405","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"}