{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837597,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 functions $\\operatorname{Park}^{(m)}(\\Phi)$. 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. In this paper we investigate the case $m=1$ for the other infinite families of root systems ($B_n$, $C_n$ and $D_n$). In each type we define models for the finite torus and for the set of non-nesting parking functions in terms of labelled lattice paths. The map $\\zeta$ can then be viewed as a map between these combinatorial objects. Our work entails new bijections between (square) lattice paths and ballot paths.<\/jats:p>","DOI":"10.37236\/6714","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:42:31Z","timestamp":1578670951000},"source":"Crossref","is-referenced-by-count":0,"title":["On Parking Functions and the Zeta Map in Types B, C and D"],"prefix":"10.37236","volume":"25","author":[{"given":"Robin","family":"Sulzgruber","sequence":"first","affiliation":[]},{"given":"Marko","family":"Thiel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,1,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:41:38Z","timestamp":1579236098000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6714","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,1,12]]},"article-number":"P1.8"}}