{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:16:12Z","timestamp":1759335372251,"version":"3.37.3"},"reference-count":19,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T00:00:00Z","timestamp":1707955200000},"content-version":"vor","delay-in-days":45,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2024,1,11]]},"published-print":{"date-parts":[[2024]]},"abstract":"<jats:p>We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a consecutive pattern of length at most three. For each pattern <jats:italic>p<\/jats:italic>, we provide a bivariate generating function, where the coefficient <jats:italic>c<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>n,k<\/jats:italic>) of <jats:italic>x<\/jats:italic><jats:sup><jats:italic>n<\/jats:italic><\/jats:sup><jats:italic>y<\/jats:italic><jats:sup><jats:italic>k<\/jats:italic><\/jats:sup> in its series expansion is the number of length <jats:italic>n<\/jats:italic> Catalan words avoiding <jats:italic>p<\/jats:italic> and ending with the symbol <jats:italic>k<\/jats:italic>. We deduce recurrence relations or closed forms for <jats:italic>c<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>n<\/jats:italic>, <jats:italic>k<\/jats:italic>) and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding <jats:italic>p<\/jats:italic>. Finally, we characterize the sequence <jats:italic>c<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>n<\/jats:italic>, <jats:italic>k<\/jats:italic>) using Riordan arrays.<\/jats:p>","DOI":"10.1051\/ita\/2024001","type":"journal-article","created":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T09:01:05Z","timestamp":1707987665000},"page":"1","source":"Crossref","is-referenced-by-count":2,"title":["Consecutive pattern-avoidance in Catalan words according to the last symbol"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9811-8028","authenticated-orcid":false,"given":"Jean-Luc","family":"Baril","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5587-2178","authenticated-orcid":false,"given":"Daniela","family":"Colmenares","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8028-9312","authenticated-orcid":false,"given":"Jos\u00e9 L.","family":"Ram\u00edrez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2278-5744","authenticated-orcid":false,"given":"Emmanuel D.","family":"Silva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lina M.","family":"Simbaqueba","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diana A.","family":"Toquica","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,2,15]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Stanley R., Catalan Numbers. 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