{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:13:31Z","timestamp":1767237211109,"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>Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation.  We investigate the proper way to adapt this tool when working with multi-equation recursive systems. \t\t\t\t\t\t Given an irreducible non-negative power series system with $m$ equations, let $\\rho$ be the radius of convergence of the solution power series and let $\\pmb{\\tau}$ be the values of the solution series evaluated at $\\rho$.  The main results of the paper include:  (a) the set of characteristic points form an antichain in ${\\mathbb R}^{m+1}$, (b) given a characteristic point $(a,\\mathbf{b})$, (i) the spectral radius of the Jacobian of $\\pmb \\gamma$ at $(a, \\mathbf{b})$ is $\\ge 1$, and (ii) it is $=1$ iff $(a,\\mathbf{b}) = (\\rho,\\pmb{\\tau})$, (c) if $(\\rho,\\pmb{\\tau})$ is a characteristic point, then (i) $\\rho$ is the largest $a$ for $(a,\\mathbf{b})$ a characteristic point, and (ii) a characteristic point $(a,\\mathbf{b})$ with $a=\\rho$ is the extreme point $(\\rho,\\pmb{\\tau})$. <\/jats:p>","DOI":"10.37236\/393","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:10:09Z","timestamp":1578715809000},"source":"Crossref","is-referenced-by-count":5,"title":["Characteristic Points of Recursive Systems"],"prefix":"10.37236","volume":"17","author":[{"given":"Jason P.","family":"Bell","sequence":"first","affiliation":[]},{"given":"Stanley N.","family":"Burris","sequence":"additional","affiliation":[]},{"given":"Karen A.","family":"Yeats","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,9,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r121\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:27:33Z","timestamp":1579303653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/393","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,9,1]]},"article-number":"R121"}}