{"paper":{"title":"A new Plethystic Symmetric Function Operator and The rational Compositional Shuffle Conjecture at t=1/q","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. M. Garsia, E. Leven, G. Xin, N. Wallach","submitted_at":"2015-01-04T04:28:19Z","abstract_excerpt":"Our main result here is that the specialization at $t=1/q$ of the $Q_{km,kn}$ operators studied in [4] may be given a very simple plethystic form. This discovery yields elementary and direct derivations of several identities relating these operators at $t=1/q$ to the Rational Compositional Shuffle conjecture of [3]. In particular we show that if $m,n $ and $k$ are positive integers and $(m,n)$ is a coprime pair then $$ q^{(km-1)(kn-1)+k-1\\over 2} Q_{km,kn}(-1)^{kn}\\Big|_{t=1/q} \\,=\\, \\textstyle{[k]_q\\over [km]_q} e_{km}\\big[ X[km]_q\\big] $$ where as customarily, for any integer $s \\geq 0$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00631","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"}