{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837351,"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>We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes the $\\mathfrak{DI}$ machine introduced by Rebecca Smith, which studies the case $k=1$. Here we show that, for $k=2$, the set of sortable\u00a0 permutations is a class with infinite basis, by explicitly finding an antichain of minimal nonsortable permutations. This construction can easily be adapted to each $k\\geqslant 3$. Next we describe an optimal sorting algorithm, again for the case $k=2$. We then analyze two types of left-greedy sorting procedures, obtaining complete results in one case and only some partial results in the other one. We close the paper by discussing a few open questions.<\/jats:p>","DOI":"10.37236\/9154","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:54:27Z","timestamp":1578617667000},"source":"Crossref","is-referenced-by-count":2,"title":["Stack Sorting with Increasing and Decreasing Stacks"],"prefix":"10.37236","volume":"27","author":[{"given":"Giulio","family":"Cerbai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lapo","family":"Cioni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Ferrari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p1\/7986","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p1\/7986","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T22:59:04Z","timestamp":1579215544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9154","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,10]]},"article-number":"P1.1"}}