{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T21:53:20Z","timestamp":1648936400633},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> A substring w[i.j] in w is called a repetition of period p if w[k] = w[k + p] for any i \u2264 k \u2264 j - p. Especially, a maximal repetition, which cannot be extended neither to left nor to right, is called a run. The ratio of the length of the run to its period, i.e. [Formula: see text], is called an exponent. The sum of exponents of runs in a string is of interest. The maximal value of the sum is still unknown, and the current upper bound is 2.9n given by Crochemore and Ilie, where n is the length of a string. In this paper we show a closed formula which exactly expresses the average value of it for any n and any alphabet size, and the limit of this value per unit length as n approaches infinity. For binary strings, the limit value is approximately 1.13103. We also show the average number of squares in a string of length n and its limit value. <\/jats:p>","DOI":"10.1142\/s0129054109007078","type":"journal-article","created":{"date-parts":[[2009,11,23]],"date-time":"2009-11-23T01:28:50Z","timestamp":1258939730000},"page":"1135-1146","source":"Crossref","is-referenced-by-count":1,"title":["AVERAGE VALUE OF SUM OF EXPONENTS OF RUNS IN A STRING"],"prefix":"10.1142","volume":"20","author":[{"given":"KAZUHIKO","family":"KUSANO","sequence":"first","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan"}]},{"given":"WATARU","family":"MATSUBARA","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan"}]},{"given":"AKIRA","family":"ISHINO","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan"}]},{"given":"AYUMI","family":"SHINOHARA","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(81)90024-7"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326019"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107341005"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.04.020"},{"key":"rf10","first-page":"45","volume":"42","author":"Puglisi S. J.","journal-title":"Australasian Journal of Combinatorics"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2007.01.007"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054109007078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:36:12Z","timestamp":1565094972000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054109007078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":6,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1142\/S0129054109007078"],"URL":"https:\/\/doi.org\/10.1142\/s0129054109007078","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}