{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834773,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we show how general determinants may be viewed as generating functions of\u00a0nonintersecting lattice paths, using the\u00a0Lindstr\u00f6m-Gessel-Viennot-method\u00a0and the Jacobi Trudi identity together with elementary observations.After some preparations, this point of view provides \"graphical proofs''\u00a0for classical determinantal identities like the Cauchy-Binet formula, Dodgson's\u00a0condensation formula, the Pl\u00fccker relations, Laplace's expansion and Turnbull's identity.\u00a0Also, a determinantal identity generalizing Dodgson's condensation formula is presented,\u00a0which might be new.<\/jats:p>","DOI":"10.37236\/2530","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:25:16Z","timestamp":1578713116000},"source":"Crossref","is-referenced-by-count":1,"title":["Viewing Determinants as Nonintersecting Lattice Paths yields Classical Determinantal Identities Bijectively"],"prefix":"10.37236","volume":"19","author":[{"given":"Markus","family":"Fulmek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,8,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:31:32Z","timestamp":1579300292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/2530","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,8,16]]},"article-number":"P21"}}