{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:40:39Z","timestamp":1767987639386,"version":"3.49.0"},"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>We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fractions with coefficients that are quasi-affine of period 2. Our proofs are based on bijections from trees to labeled Motzkin or Schr\u00f6der paths; these bijections extend the well-known bijection of Fran\u00e7on--Viennot (1979) interpreted in terms of increasing binary trees. This work can also be viewed as a sequel to the recent work of Elvey Price and Sokal (2020), where they provide combinatorial interpretations for Thron-type continued fractions with coefficients that are affine. Towards the end of the paper, we conjecture an equidistribution of vincular patterns on permutations.<\/jats:p>","DOI":"10.37236\/13670","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:27Z","timestamp":1767969147000},"source":"Crossref","is-referenced-by-count":0,"title":["Thron-Type Continued Fractions (T-Fractions) for Some Classes of Increasing Trees"],"prefix":"10.37236","volume":"33","author":[{"given":"Veronica","family":"Bitonti","sequence":"first","affiliation":[]},{"given":"Bishal","family":"Deb","sequence":"additional","affiliation":[]},{"given":"Alan D.","family":"Sokal","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,1,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:27Z","timestamp":1767969147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/13670","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,9]]},"article-number":"P1.5"}}