{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:18:50Z","timestamp":1759335530046},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7529,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1986,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is proved that the <jats:italic>d<\/jats:italic>th highest leaf, where all planted plane trees with <jats:italic>n<\/jats:italic> nodes are assumed to be equally likely, has an average height <jats:styled-content>\\documentclass{article}\\pagestyle{empty}\\begin{document}$ \\sqrt {\\pi n} &amp;#x02010; \\frac{1}{2} &amp;#x02010; \\frac{2}{3}\\sum\\nolimits_{s = 1}^{d &amp;#x02010; 1} {\\left({2\/9} \\right)^s \\left({\\begin{array}{*{20}c} {2s + 1} \\\\ s \\\\ \\end{array}} \\right)} + O\\left({n^{&amp;#x02010; 1\/2 + \\varepsilon}} \\right) $\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content> for all \u03f5 &gt; 0 and <jats:italic>n<\/jats:italic> \u2192 \u221e. This solves a problem left open in one of our previous papers.<\/jats:p>","DOI":"10.1002\/net.3230160107","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T20:22:00Z","timestamp":1178914920000},"page":"67-75","source":"Crossref","is-referenced-by-count":3,"title":["The average height of the <i>d<\/i>\u2010th highest leaf of a planted plane tree"],"prefix":"10.1002","volume":"16","author":[{"given":"Helmut","family":"Prodinger","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"15","volume-title":"The average height of planted plane trees. I. Graph Theory and Computing","author":"De Bruijn N. G.","year":"1972"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90004-6"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579315"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90019-9"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","volume-title":"On the number of deepest nodes in ordered trees","author":"Kemp R.","DOI":"10.1016\/0012-365X(90)90064-O"},{"key":"e_1_2_1_7_2","volume-title":"The Art of Computer Programming","author":"Knuth D. E.","year":"1973"},{"key":"e_1_2_1_8_2","first-page":"51","article-title":"The height of planted plane trees revisited","volume":"16","author":"Prodinger H.","year":"1983","journal-title":"Am Combinatoria"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(84)80038-4"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230160107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230160107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T01:50:50Z","timestamp":1697853050000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230160107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,3]]}},"alternative-id":["10.1002\/net.3230160107"],"URL":"https:\/\/doi.org\/10.1002\/net.3230160107","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,3]]}}}