{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T08:46:52Z","timestamp":1770281212823,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove that the class of permutations generated by passing an ordered sequence $12\\dots n$ through a stack of depth 2 and an infinite stack in series is in bijection with an unambiguous context-free language, where a permutation of length $n$ is encoded by a string of length $3n$. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. We use the explicit context-free grammar to compute the generating function:\\[\\sum_{n\\geq 0} c_n t^n = \\frac{(1+q)\\left(1+5q-q^2-q^3-(1-q)\\sqrt{(1-q^2)(1-4q-q^2)}\\right)}{8q}\\]where $c_n$ is the number of permutations of length $n$ that can be generated, and $q \\equiv q(t) = \\frac{1-2t-\\sqrt{1-4t}}{2t}$ is a simple variant of the Catalan generating function. This in turn implies that $c_n^{1\/n} \\to 2+2\\sqrt{5}$.<\/jats:p>","DOI":"10.37236\/4571","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:07:35Z","timestamp":1578701255000},"source":"Crossref","is-referenced-by-count":3,"title":["Permutations Generated by a Depth 2 Stack and an Infinite Stack in Series are Algebraic"],"prefix":"10.37236","volume":"22","author":[{"given":"Murray","family":"Elder","sequence":"first","affiliation":[]},{"given":"Geoffrey","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Rechnitzer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,4,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:17:37Z","timestamp":1579256257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,29]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4571","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,29]]},"article-number":"P2.16"}}