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Our main aim is to determine the rank of the monoid [Formula: see text] of all weak endomorphisms of a directed path with [Formula: see text] vertices, which is a submonoid of the widely studied monoid [Formula: see text] of all order-preserving transformations of an [Formula: see text]-chain. Also, we describe the regular elements of [Formula: see text] and calculate its size and number of idempotents.<\/jats:p>","DOI":"10.1142\/s1793557123500699","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T16:18:51Z","timestamp":1663604331000},"source":"Crossref","is-referenced-by-count":4,"title":["On the rank of monoids of endomorphisms of a finite directed path"],"prefix":"10.1142","volume":"16","author":[{"given":"V\u00edtor H.","family":"Fernandes","sequence":"first","affiliation":[{"name":"CMA, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade NOVA de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal"}]},{"given":"T\u00e2nia","family":"Paulista","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade NOVA de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"S1793557123500699BIB001","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1017\/S0305004115000389","volume":"159","author":"Ara\u00fajo J.","year":"2015","journal-title":"Math. 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