{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:28Z","timestamp":1747189708237,"version":"3.40.5"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> Let [Formula: see text] be the standard graded polynomial ring, with K a field, and let [Formula: see text], [Formula: see text], be a [Formula: see text]-tuple whose entries are non-negative integers. To a t-spread ideal I in S, we associate a unique [Formula: see text]-vector and we prove that if I is t-spread strongly stable, then there exists a unique t-spread lex ideal which shares the same [Formula: see text]-vector of I via the combinatorics of the t-spread shadows of special sets of monomials of S. Moreover, we characterize the possible [Formula: see text]-vectors of t-vector spread strongly stable ideals generalizing the well-known theorems of Macaulay and Kruskal\u2013Katona. Finally, we prove that among all t-spread strongly stable ideals with the same [Formula: see text]-vector, the t-spread lex ideals have the largest Betti numbers. <\/jats:p>","DOI":"10.1142\/s0218196724500255","type":"journal-article","created":{"date-parts":[[2024,5,3]],"date-time":"2024-05-03T10:11:32Z","timestamp":1714731092000},"page":"571-590","source":"Crossref","is-referenced-by-count":0,"title":["Macaulay\u2019s theorem for vector-spread algebras"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8140-7248","authenticated-orcid":false,"given":"Marilena","family":"Crupi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d\u2019Alcontres 31, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6205-9524","authenticated-orcid":false,"given":"Antonino","family":"Ficarra","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d\u2019Alcontres 31, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4030-3706","authenticated-orcid":false,"given":"Ernesto","family":"Lax","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d\u2019Alcontres 31, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,6,8]]},"reference":[{"doi-asserted-by":"publisher","key":"S0218196724500255BIB001","DOI":"10.1142\/S0218196722500357"},{"issue":"110","key":"S0218196724500255BIB002","first-page":"107","volume":"62","author":"Andrei-Ciobanu C.","year":"2019","journal-title":"Bull. 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