{"paper":{"title":"On parking functions and the zeta map in types B,C and D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marko Thiel, Robin Sulzgruber","submitted_at":"2016-09-11T07:19:10Z","abstract_excerpt":"Let $\\Phi$ be an irreducible crystallographic root system with Weyl group $W$, coroot lattice $\\check{Q}$ and Coxeter number $h$. Recently the second named author defined a uniform $W$-isomorphism $\\zeta$ between the finite torus $\\check{Q}/(mh+1)\\check{Q}$ and the set of non-nesting parking fuctions $\\operatorname{Park}^{(m)}(\\Phi)$. If $\\Phi$ is of type $A_{n-1}$ and $m=1$ this map is equivalent to a map defined on labelled Dyck paths that arises in the study of the Hilbert series of the space of diagonal harmonics.\n  In this paper we investigate the case $m=1$ for the other infinite familie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03128","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"}