{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T04:29:26Z","timestamp":1761884966713,"version":"build-2065373602"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"Scientific and Technological Research Council of Turkey T\u00dcB\u0130TAK","award":["124F113"],"award-info":[{"award-number":["124F113"]}]},{"name":"Anusandhan National Research Foundation","award":["CRG\/2023\/007668"],"award-info":[{"award-number":["CRG\/2023\/007668"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>In this paper, we prove the conjectures of Gharakhloo and Welker [S. Gharakhloo and V. Welker, Hypergraph LSS-ideals and coordinate sections of symmetric tensors, Commun. Algebra\u00a051(8) (2023) 3299\u20133309, Conjectures\u00a03.5 and\u00a03.6] that the positive matching decomposition number [Formula: see text] of a [Formula: see text]-uniform hypergraph is bounded from above by a polynomial of degree [Formula: see text] in terms of the number of vertices. Moreover, we derive a lower bound for [Formula: see text] specifically for complete [Formula: see text]-uniform hypergraphs. Additionally, we obtain an upper bound for [Formula: see text] of r-uniform hypergraphs. As an application from an algebraic point of view, we obtain the radical, complete intersection, and prime properties of Lov\u00e1sz\u2013Saks\u2013Schrijver (LSS) ideals of r-uniform hypergraphs. For an r-uniform hypergraphs [Formula: see text] such that [Formula: see text] for all [Formula: see text], we give a characterization of positive matching in terms of strong alternate closed walks. For a specific class of hypergraphs, we classify the radical and complete intersection properties of LSS ideals.<\/jats:p>","DOI":"10.1142\/s0218196725500390","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T04:26:11Z","timestamp":1758515171000},"page":"1181-1203","source":"Crossref","is-referenced-by-count":0,"title":["On positive matching decomposition conjectures of hypergraphs"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3910-247X","authenticated-orcid":false,"given":"Marie Amalore","family":"Nambi","sequence":"first","affiliation":[{"name":"Faculty of Engineering and Natural Sciences, Sabanci University, Orta Mahalle, Tuzla, 34956 Istanbul, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1144-2096","authenticated-orcid":false,"given":"Neeraj","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,10,8]]},"reference":[{"key":"S0218196725500390BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-014-1150-3"},{"key":"S0218196725500390BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2007.09.014"},{"issue":"11","key":"S0218196725500390BIB003","first-page":"3245","volume":"2015","author":"Conca A.","year":"2015","journal-title":"Int. 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