Extremal Betti Numbers of t-Spread Strongly Stable Ideals

Luca Amata and Marilena Crupi
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Luca Amata: Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
Marilena Crupi: Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy

Mathematics, 2019, vol. 7, issue 8, 1-16

Abstract: Let K be a field and let S = K [ x 1 , ? , x n ] be a polynomial ring over K . We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t -spread strongly stable ideals, where t is an integer ≥ 1 . A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the t -spread strongly stable ideals with the maximal number of extremal Betti numbers when t = 2 .

Keywords: graded ideals; squarefree monomial ideals; minimal graded resolutions; extremal Betti numbers; t-spread monomial ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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