{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T13:20:53Z","timestamp":1758979253167},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p> Mateescu et al (2000) introduced an interesting new tool, called Parikh matrix, to study in terms of subwords, the numerical properties of words over an alphabet. The Parikh matrix gives more information than the well-known Parikh vector of a word which counts only occurrences of symbols in a word. In this note a property of two words u, \u03c5, called \"ratio property\", is introduced. This property is a sufficient condition for the words u\u03c5 and \u03c5u to have the same Parikh matrix. Thus the ratio property gives information on the M\u2013ambiguity of certain words and certain sets of words. In fact certain regular, context-free and context-sensitive languages that have the same set of Parikh matrices are exhibited. In the study of fair words, Cerny (2006) introduced another kind of matrix, called the p\u2013matrix of a word. Here a \"weak-ratio property\" of two words u, \u03c5 is introduced. This property is a sufficient condition for the words u\u03c5 and \u03c5u to have the same p\u2013matrix. Also the words u\u03c5 and \u03c5u are fair whenever u, \u03c5 are fair and have the weak ratio property. <\/jats:p>","DOI":"10.1142\/s0129054109006528","type":"journal-article","created":{"date-parts":[[2009,4,7]],"date-time":"2009-04-07T08:25:36Z","timestamp":1239092736000},"page":"211-219","source":"Crossref","is-referenced-by-count":22,"title":["ON PARIKH MATRICES"],"prefix":"10.1142","volume":"20","author":[{"given":"K. G.","family":"SUBRAMANIAN","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"}]},{"given":"ANG MIIN","family":"HUEY","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"}]},{"given":"ATULYA K.","family":"NAGAR","sequence":"additional","affiliation":[{"name":"Deanery of Business and Computer Sciences, Liverpool Hope University, Hope Park, Liverpool L16 9JD, UK"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054107004735"},{"key":"rf2","first-page":"1","volume":"46","author":"Atanasiu A.","journal-title":"Fund. Inform."},{"key":"rf3","first-page":"783","volume":"7","author":"Atanasiu A.","journal-title":"J. Universal Comput. Sci."},{"key":"rf4","author":"Atanasiu A.","journal-title":"Theor. Comput. Sci."},{"key":"rf6","first-page":"65","volume":"73","author":"Ding C.","journal-title":"Fund. Inform."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/9789812773036_0007"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2004.06.011"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054104002418"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1051\/ita:2001131"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1145\/321356.321364"},{"key":"rf13","volume-title":"Formal Languages","author":"Salomaa A.","year":"1973"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.03.024"},{"key":"rf15","first-page":"391","volume":"64","author":"Salomaa A.","journal-title":"Fundam. Inf."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.06.025"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054109006528","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:40:06Z","timestamp":1565095206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054109006528"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":14,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S0129054109006528"],"URL":"https:\/\/doi.org\/10.1142\/s0129054109006528","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}