On the Betti numbers of monomial ideals and their powers

Reza Abdolmaleki; Rashid Zaare-Nahandi

On the Betti numbers of monomial ideals and their powers

Commutative Algebra 2022-12-27 v1

Authors: Reza Abdolmaleki , Rashid Zaare-Nahandi

Abstract

Let $S=\mathbb{K}[x_1,\ldots,x_n]$ the polynomial ring over a field $\mathbb{K}$ . In this paper for some families of monomial ideals $I \subset S$ we study the minimal number of generators of $I^k$ . We use this results to find some other Betti numbers of these families of ideals for special choices of $n$ , the number of variables.

Keywords

monomial ideals betti numbers powers of ideals minimal generators polynomial ring

Cite

@article{arxiv.2212.12828,
  title  = {On the Betti numbers of monomial ideals and their powers},
  author = {Reza Abdolmaleki and Rashid Zaare-Nahandi},
  journal= {arXiv preprint arXiv:2212.12828},
  year   = {2022}
}

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