{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:14Z","timestamp":1753893794257,"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>We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length $n$ and the set of parking functions of length $n$. For all $u$ and $v=0,1,2,3$ and all $n\\le 7$ we describe in terms of admissible pairs the dimensions of the  bi-graded components $h_{u,v}$ of diagonal harmonics ${\\Bbb{C}}[x_1,\\dots,x_n;y_1,\\dots,y_n]\/S_n$, i.e., polynomials in two groups of $n$ variables modulo the diagonal action of symmetric group $S_n$.<\/jats:p>","DOI":"10.37236\/1716","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:29:02Z","timestamp":1578709742000},"source":"Crossref","is-referenced-by-count":0,"title":["Coding Parking Functions by Pairs of Permutations"],"prefix":"10.37236","volume":"10","author":[{"given":"Yurii","family":"Burman","sequence":"first","affiliation":[]},{"given":"Michael","family":"Shapiro","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,5,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:07:54Z","timestamp":1579324074000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1716","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,5,20]]},"article-number":"R23"}}