{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T22:05:17Z","timestamp":1772057117993,"version":"3.50.1"},"reference-count":4,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4782,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u03c7 be an irreducible character of the symmetric group <jats:italic>S<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. For an <jats:italic>n<\/jats:italic>\u2010by\u2010<jats:italic>n<\/jats:italic> matrix <jats:italic>A<\/jats:italic> = (<jats:italic>a<\/jats:italic><jats:sub><jats:italic>ij<\/jats:italic><\/jats:sub>), define <jats:disp-formula>\n<jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" position=\"anchor\" xlink:href=\"urn:x-wiley:03649024:media:JGT3190170404:nueq001\"><jats:alt-text>equation image<\/jats:alt-text><\/jats:graphic>\n<\/jats:disp-formula><\/jats:p><jats:p>If <jats:italic>G<\/jats:italic> is a graph, let <jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>) be the diagonal matrix of its vertex degrees and <jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>) its adjacency matrix. Let <jats:italic>y<\/jats:italic> and <jats:italic>z<\/jats:italic> be independent indeterminates, and define <jats:italic>L<\/jats:italic>(<jats:italic>G<\/jats:italic>) = <jats:italic>yD<\/jats:italic>(<jats:italic>G<\/jats:italic>) + <jats:italic>zA<\/jats:italic>(<jats:italic>G<\/jats:italic>). Suppose <jats:italic>t<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> is the number of trees on <jats:italic>n<\/jats:italic> vertices and <jats:italic>s<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> is the number of such trees <jats:italic>T<\/jats:italic> for which there exists a nonisomorphic tree <jats:italic>T\u0303<\/jats:italic> such that <jats:italic>d<\/jats:italic><jats:sub>\u03c7<\/jats:sub>(<jats:italic>xl \u2010 L<\/jats:italic>(<jats:italic>T<\/jats:italic>)) = <jats:italic>d<\/jats:italic><jats:sub><jats:italic>x<\/jats:italic><\/jats:sub>(<jats:italic>xl \u2010 L<\/jats:italic>(<jats:italic>T\u0303<\/jats:italic>)) for every irreducible character \u03c7 of <jats:italic>S<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. Then lim<jats:sub><jats:italic>n<\/jats:italic>\u2192\u221e<\/jats:sub> <jats:italic>S<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>\/<jats:italic>t<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> = 1. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170404","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:16:43Z","timestamp":1180185403000},"page":"467-476","source":"Crossref","is-referenced-by-count":22,"title":["Almost all trees share a complete set of immanantal polynomials"],"prefix":"10.1002","volume":"17","author":[{"given":"Phillip","family":"Botti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Russell","family":"Merris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Spectra of Graphs","author":"Cvetkovi\u0107 D. M.","year":"1979"},{"key":"e_1_2_1_3_2","first-page":"219","article-title":"On the spectral characteristics of trees","volume":"3","author":"McKay B. D.","year":"1977","journal-title":"Ars Combinat."},{"key":"e_1_2_1_4_2","first-page":"275","volume-title":"New Directions in the Theory of Graphs","author":"Schwenk A. J.","year":"1973"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0116041"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T03:21:19Z","timestamp":1698204079000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["10.1002\/jgt.3190170404"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170404","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}