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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.03128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-11T07:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"32c89988235d81b5e9007cf5e0d60e44bdcbc272d5c9fa51396f7b6515022034","abstract_canon_sha256":"3f86add297fbb2eef3e286085fc5fe78e957f266c49af1f55d70a039c6ebcc57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:47.711534Z","signature_b64":"/mjfjyypRxYQJ7aMjEBUEQ/E3w0+cwEsO2qr/UtQhEvbqoYYshIcl80GV4dG6BBJ24EN868RpDSHBd+T4gBiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57df09c9501b345b355aecb19e99a83c52cbbfbcb608d0eaa7b009eb260192f1","last_reissued_at":"2026-05-18T01:04:47.710943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:47.710943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $h$. 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