{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T18:01:46Z","timestamp":1777744906153,"version":"3.51.4"},"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>We give a positive answer to a question raised by Davis et al. (Discrete Mathematics\u00a0341, 2018), concerning permutations with the same\u00a0 $\\pi_{i-1}&lt;\\pi_i&gt;\\pi_{i+1}$. The question is: given $\\pi,\\pi'\\in S_n$ with the same pinnacle set $S$, is there a sequence of operations that transforms $\\pi$ into $\\pi'$ such that all the intermediate permutations have pinnacle set $S$? We introduce {\\em balanced reversals}, defined as reversals that do not modify the pinnacle set of the permutation to which they are applied. Then we show that $\\pi$ may be sorted by balanced reversals (i.e. transformed into a standard permutation $Id_S$), implying that $\\pi$ may be transformed into $\\pi'$ using at most $4n-2\\min\\{p,3\\}$ balanced reversals, where $p=|S|\\geq 1$. In case $p=0$, at most $2n-1$ balanced reversals are needed.<\/jats:p>","DOI":"10.37236\/9231","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:06Z","timestamp":1599187686000},"source":"Crossref","is-referenced-by-count":2,"title":["Sorting Permutations with Fixed Pinnacle Set"],"prefix":"10.37236","volume":"27","author":[{"given":"Irena","family":"Rusu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p23\/8141","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p23\/8141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:06Z","timestamp":1599187686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,7]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9231","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,7]]},"article-number":"P3.23"}}