{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:09:40Z","timestamp":1758672580508,"version":"3.44.0"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"National Research Foundation funded by the government of Korea","award":["MG094701"],"award-info":[{"award-number":["MG094701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p> The free regular \u22c6-monoid of rank r is the freest r-generated regular monoid [Formula: see text] in which every element m has a distinguished pseudo-inverse [Formula: see text] satisfying [Formula: see text] and [Formula: see text]. We study the growth rate of the monogenic regular \u22c6-monoid [Formula: see text], and prove that this growth rate is intermediate. In particular, we deduce that [Formula: see text] is not rational or automatic for any [Formula: see text], yielding the analogue of a result of Cutting and Solomon for free inverse monoids. Next, for all ranks [Formula: see text] we determine the integral homology groups [Formula: see text], and by constructing a collapsing scheme prove that they vanish in dimension [Formula: see text] and above. As a corollary, we deduce that the free regular \u22c6-monoid [Formula: see text] of rank [Formula: see text] does not have the homological finiteness property [Formula: see text], yielding the analogue of a result of Gray and Steinberg for free inverse monoids. <\/jats:p>","DOI":"10.1142\/s0218196725500213","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T05:40:11Z","timestamp":1747374011000},"page":"965-984","source":"Crossref","is-referenced-by-count":0,"title":["On the growth and integral (co)homology of free regular star-monoids"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3696-5894","authenticated-orcid":false,"given":"Carl-Fredrik","family":"Nyberg-Brodda","sequence":"first","affiliation":[{"name":"June E. 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