{"paper":{"title":"A refinement of the Shuffle Conjecture with cars of two sizes and $t=1/q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angela Hicks, Emily Leven","submitted_at":"2013-04-25T20:47:22Z","abstract_excerpt":"The original Shuffle Conjecture of Haglund et al. has a symmetric function side and a combinatorial side. The symmetric function side may be simply expressed as $<\\nabla e_n, h_{\\mu}>$ where \\nabla is the Macdonald polynomial eigen-operator of Bergeron and Garsia and $h_\\mu$ is the homogeneous basis indexed by $\\mu=(\\mu_1,\\mu_2,...,\\mu_k)$ partitions of n. The combinatorial side q,t-enumerates a family of Parking Functions whose reading word is a shuffle of k successive segments of 1,2,3,...,n of respective lengths $\\mu_1,\\mu_2,...,\\mu_k$. It can be shown that for t=1/q the symmetric function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7026","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"}