{"paper":{"title":"The descent set polynomial revisited","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":"2014-08-28T20:30:43Z","abstract_excerpt":"We continue to explore cyclotomic factors in the descent set polynomial $Q_{n}(t)$, which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form $\\Phi_{2s}$ or $\\Phi_{4s}$ where $s$ is an odd integer, with many of these being of the form $\\Phi_{2p}$ where $p$ is a prime. We also show that if $\\Phi_{2}$ is a factor of $Q_{2n}(t)$ then it is a double factor. Finally, we give conditions for an odd prime power $q = p^{r}$ for which $\\Phi_{2p}$ is a double factor of $Q_{2q}(t)$ and of $Q_{q+1}(t)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6858","kind":"arxiv","version":2},"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"}