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Cohen–Macaulayness of Vertex Splittable Monomial Ideals

Author

Listed:
  • Marilena Crupi

    (Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
    These authors contributed equally to this work.
    These authors are members of GNSAGA of INDAM (Italy).)

  • Antonino Ficarra

    (Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
    These authors contributed equally to this work.
    These authors are members of GNSAGA of INDAM (Italy).)

Abstract

In this paper, we give a new criterion for the Cohen–Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of checking the Cohen–Macaulay property. As a result, we obtain characterizations for Gorenstein, level and pseudo-Gorenstein vertex splittable ideals. Furthermore, we provide new and simpler combinatorial proofs of known Cohen–Macaulay criteria for several families of monomial ideals, such as (vector-spread) strongly stable ideals and (componentwise) polymatroidals. Finally, we characterize the family of bi-Cohen–Macaulay graphs by the novel criterion for the Cohen–Macaulayness of vertex splittable ideals.

Suggested Citation

  • Marilena Crupi & Antonino Ficarra, 2024. "Cohen–Macaulayness of Vertex Splittable Monomial Ideals," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:912-:d:1360299
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