{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814406,"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>A positive linear fractional transformation (PLFT) is a function of the form $f(z)=\\frac{az+b}{cz+d}$ where $a,b,c$ and $d$ are nonnegative integers with determinant $ad-bc\\neq 0$.\u00a0Nathanson generalized the notion of the Calkin-Wilf tree to PLFTs and used it to partition the set of PLFTs into an infinite forest of rooted trees. The roots of these PLFT Calkin-Wilf trees are called orphans. In this paper, we provide a combinatorial formula for the number of orphans with fixed determinant $D$. In addition, we derive a method for determining the orphan ancestor of a given PLFT. Lastly, taking $z$ to be a complex number, we show that every positive complex number has finitely many ancestors in the forest of complex $(u,v)$-Calkin-Wilf trees.<\/jats:p>","DOI":"10.37236\/5684","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:51:08Z","timestamp":1578689468000},"source":"Crossref","is-referenced-by-count":1,"title":["Orphans in Forests of Linear Fractional Transformations"],"prefix":"10.37236","volume":"23","author":[{"given":"Sandie","family":"Han","sequence":"first","affiliation":[]},{"given":"Ariane M.","family":"Masuda","sequence":"additional","affiliation":[]},{"given":"Satyanand","family":"Singh","sequence":"additional","affiliation":[]},{"given":"Johann","family":"Thiel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,7,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:27:16Z","timestamp":1579238836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,8]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5684","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,7,8]]},"article-number":"P3.6"}}