{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T14:46:28Z","timestamp":1777301188967,"version":"3.51.4"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"Vietnam Ministry of Education and Training","award":["B2022-SPH-02"],"award-info":[{"award-number":["B2022-SPH-02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> Let [Formula: see text] be a two-dimensional squarefree monomial ideal in a polynomial ring [Formula: see text], where [Formula: see text] is a field. In this paper, we give explicit formulas for the extremal Betti numbers of the [Formula: see text]th symbolic power of [Formula: see text] for all [Formula: see text]. As a consequence, we characterize the rings [Formula: see text] which are pseudo-Gorenstein as sense of Ene et al. [Pseudo-Gorenstein and level Hibi rings, J. Algebra 431 (2015) 138\u2013161]. We also provide a complete classification for the level property of the second symbolic power [Formula: see text]. In particular, we obtain a new algebraic-property of the unknown Moore graph of degree 57. <\/jats:p>","DOI":"10.1142\/s0218196722500448","type":"journal-article","created":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T12:58:41Z","timestamp":1652101121000},"page":"1043-1069","source":"Crossref","is-referenced-by-count":2,"title":["Extremal Betti numbers of symbolic powers of two-dimensional squarefree monomial ideals"],"prefix":"10.1142","volume":"32","author":[{"given":"Nguy\u00ean","family":"Quang L\u00f4c","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam"}]},{"given":"Nguy\u00ean","family":"C\u00f4ng Minh","sequence":"additional","affiliation":[{"name":"School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam"}]},{"given":"Phan","family":"Thi Thuy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam"}]}],"member":"219","published-online":{"date-parts":[[2022,5,6]]},"reference":[{"key":"S0218196722500448BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1999.7970"},{"key":"S0218196722500448BIB002","doi-asserted-by":"publisher","DOI":"10.1201\/9781420050912.ch1"},{"key":"S0218196722500448BIB003","volume-title":"Graph Theory","author":"Diestel R.","year":"2000","edition":"2"},{"key":"S0218196722500448BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(84)90092-9"},{"key":"S0218196722500448BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2015.02.002"},{"key":"S0218196722500448BIB006","doi-asserted-by":"publisher","DOI":"10.1216\/JCA-2016-8-1-77"},{"key":"S0218196722500448BIB007","doi-asserted-by":"publisher","DOI":"10.1147\/rd.45.0497"},{"key":"S0218196722500448BIB009","volume-title":"Combinatorial Commutative Algebra","author":"Miller E.","year":"2004"},{"key":"S0218196722500448BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2019.05.044"},{"key":"S0218196722500448BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2009.09.014"},{"key":"S0218196722500448BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0346-0329-4_4"},{"key":"S0218196722500448BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1220-1_3"},{"key":"S0218196722500448BIB014","volume-title":"Combinatorics and Commutative Algebra","author":"Stanley R.","year":"1996","edition":"2"},{"issue":"96","key":"S0218196722500448BIB015","first-page":"327","volume":"48","author":"Takayama Y.","year":"2005","journal-title":"Bull. Math. Soc. Sci. Math. Roumanie (N. S.)"},{"key":"S0218196722500448BIB016","doi-asserted-by":"publisher","DOI":"10.1201\/b18224"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500448","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T08:34:59Z","timestamp":1655886899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196722500448"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":15,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1142\/S0218196722500448"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500448","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,6]]}}}