• Pavinder Singh

      Articles written in Proceedings – Mathematical Sciences

    • Deficiently Extremal Cohen-Macaulay Algebras

      Chanchal Kumar Pavinder Singh

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      The aim of this paper is to study homological properties of deficiently extremal Cohen–Macaulay algebras. Eagon–Reiner showed that the Stanley–Reisner ring of a simplicial complex has a linear resolution if and only if the Alexander dual of the simplicial complex is Cohen–Macaulay. An extension of a special case of Eagon–Reiner theorem is obtained for deficiently extremal Cohen–Macaulay Stanley–Reisner rings.

    • Deficiently Extremal Gorenstein Algebras

      Pavinder Singh

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      The aim of this article is to study the homological properties of deficiently extremal Gorenstein algebras. We prove that if $R/I$ is an odd deficiently extremal Gorenstein algebra with pure minimal free resolution, then the codimension of $R/I$ must be odd. As an application, the structure of pure minimal free resolution of a nearly extremal Gorenstein algebra is obtained.

    • On Betti numbers in the linear strand and regularity of triangular graphs

      SHAHNAWAZ AHMAD RATHER PAVINDER SINGH ROHIT VERMA

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      To every finite simple graph $G$, we associate the so-called edge ideal $I (G)$, which is a square-free quadratic monomial ideal generated by the monomials corresponding to the edges of $G$. In this paper, we determine all the initial graded Betti numbers of edge ideals of triangular graphs and alternate triangular graphs in terms of the underlying graph. We also compute the regularity of edge ideals of triangular and alternate triangular graphs.

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