{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:14Z","timestamp":1740155954946,"version":"3.37.3"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> A permutation over alphabet [Formula: see text] is a sequence over [Formula: see text], where every element occurs exactly once. [Formula: see text] denotes symmetric group defined over [Formula: see text]. [Formula: see text] denotes the Identity permutation. [Formula: see text] is the reverse permutation i.e., [Formula: see text]. An operation, that we call as an LE operation, has been defined which consists of exactly two generators: set-rotate that we call Rotate and pair-exchange that we call Exchange (OEIS). At least two generators are the required to generate [Formula: see text]. Rotate rotates all elements to the left (moves leftmost element to the right end) and Exchange is the pair-wise exchange of the two leftmost elements. The optimum number of moves for transforming [Formula: see text] into [Formula: see text] with LE operation are known for [Formula: see text]; as listed in OEIS with identity A048200. However, no general upper bound is known. The contributions of this article are: (a) a novel upper bound for the number of moves required to sort [Formula: see text] with LE has been derived; (b) the optimum number of moves to sort the next larger [Formula: see text] i.e., [Formula: see text] has been computed; (c) an algorithm conjectured to compute the optimum number of moves to sort a given [Formula: see text] has been designed. <\/jats:p>","DOI":"10.1142\/s1793830920500330","type":"journal-article","created":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T07:59:17Z","timestamp":1581580757000},"page":"2050033","source":"Crossref","is-referenced-by-count":2,"title":["Exact upper bound for sorting Rn with LE"],"prefix":"10.1142","volume":"12","author":[{"given":"Sai Satwik","family":"Kuppili","sequence":"first","affiliation":[{"name":"Dept. of Computer Science and Engineering, Amrita Vishwa Vidyapeetham, Amritapuri, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8768-9183","authenticated-orcid":false,"given":"Bhadrachalam","family":"Chitturi","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science, University of Texas at Dallas, Richardson, TX, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,5,4]]},"reference":[{"key":"S1793830920500330BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/12.21148"},{"key":"S1793830920500330BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(96)00069-8"},{"key":"S1793830920500330BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830911001206"},{"journal-title":"Theoret. Comput. Sci.","year":"2018","author":"Chitturi B.","key":"S1793830920500330BIB006"},{"key":"S1793830920500330BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.04.045"},{"key":"S1793830920500330BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.04.025"},{"key":"S1793830920500330BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-5913-3_81"},{"issue":"0","key":"S1793830920500330BIB012","first-page":"205","volume":"15","author":"Gostevsky D. A.","year":"2018","journal-title":"Discr. math. Math. Cybernet."},{"key":"S1793830920500330BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(85)90047-7"},{"key":"S1793830920500330BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(93)90054-O"},{"key":"S1793830920500330BIB016","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972717000028"},{"key":"S1793830920500330BIB018","first-page":"1","author":"Zhang T.","year":"2018","journal-title":"J. Algebr. Combinat."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500330","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T10:50:19Z","timestamp":1594205419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500330"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,4]]},"references-count":12,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1142\/S1793830920500330"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500330","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,5,4]]}}}