{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810581,"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 give combinatorial proofs of three identities, each of which generalizes Weyl's denominator formula for two of the three root systems $B_n$, $C_n$, $D_n$. Two of the three identities are due to S. Okada; the third appears in the author's doctoral thesis, upon which this work is based. Each of the identities we prove has a \"sum side\" and a \"product side\"; both sides are polynomials in several commuting indeterminates. We use weighted digraphs to represent the terms on each side; the set of such digraphs that corresponds to the sum side is a proper subset of the set corresponding to the product side.<\/jats:p>","DOI":"10.37236\/1236","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:26:45Z","timestamp":1578688005000},"source":"Crossref","is-referenced-by-count":2,"title":["Three generalizations of Weyl's denominator formula"],"prefix":"10.37236","volume":"3","author":[{"given":"Todd","family":"Simpson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,3,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:17:38Z","timestamp":1579310258000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1236","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1996,3,15]]},"article-number":"R12"}}