{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:28:00Z","timestamp":1760707680678},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p> We consider paths in the square lattice and use a valuation called the winding number in order to exhibit some combinatorial properties on these paths. As a corollary, we obtain a characteristic property of non-crossing closed paths, generalizing in this way a result of Daurat and Nivat (2003) on the boundary properties of polyominoes concerning salient and reentrant points. Moreover we obtain a similar result for hexagonal lattices and show that there is no other regular lattice having that property. <\/jats:p>","DOI":"10.1142\/s012905410600398x","type":"journal-article","created":{"date-parts":[[2006,6,6]],"date-time":"2006-06-06T11:11:37Z","timestamp":1149592297000},"page":"543-556","source":"Crossref","is-referenced-by-count":14,"title":["PROPERTIES OF THE CONTOUR PATH OF DISCRETE SETS"],"prefix":"10.1142","volume":"17","author":[{"given":"S.","family":"BRLEK","sequence":"first","affiliation":[{"name":"Laboratoire de Combinatoire et d Informatique Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, CP 8888, Succ. Centre-ville, Montr\u00e9al (QC) Canada H3C3P8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"LABELLE","sequence":"additional","affiliation":[{"name":"Laboratoire de Combinatoire et d Informatique Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, CP 8888, Succ. Centre-ville, Montr\u00e9al (QC) Canada H3C3P8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"LACASSE","sequence":"additional","affiliation":[{"name":"Laboratoire de Combinatoire et d Informatique Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, CP 8888, Succ. Centre-ville, Montr\u00e9al (QC) Canada H3C3P8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf3","first-page":"260","volume":"10","author":"Freeman H.","journal-title":"IRE Trans. Electronic Computer"},{"key":"rf4","unstructured":"H.\u00a0Freeman, Picture Processing and Psychopictorics, eds. B. S.\u00a0Lipkin and A.\u00a0Rosenfeld (Academic Press, New York, 1970)\u00a0pp. 241\u2013266."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1999.0488"},{"key":"rf6","first-page":"18","volume":"13","author":"Clarke A. L.","journal-title":"J. Recreational Math."},{"key":"rf8","volume-title":"Tilings and Patterns","author":"Grunbaum B.","year":"1987"},{"key":"rf9","volume-title":"Tilings and Patterns: An Introduction","author":"Grunbaum B.","year":"1989"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S012905410600398X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:28:14Z","timestamp":1565191694000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012905410600398X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":6,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1142\/S012905410600398X"],"URL":"https:\/\/doi.org\/10.1142\/s012905410600398x","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}