Dorin Popescu, Andrei Zarojanu
Abstract
Open-access reader
Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field. Suppose that $I$ is generated by one squarefree monomial of degree $ d>0$, and other squarefree monomials of degrees $\geq d+1$. If the Stanley depth of $I/J$ is $\leq d+1$ then almost always the usual depth of $I/J$ is $\leq d+1$ too.
OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field. Suppose that $I$ is generated by one squarefree monomial of degree $ d>0$, and other squarefree monomials of degrees $\geq d+1$. If the Stanley depth of $I/J$ is $\leq d+1$ then almost always the usual depth of $I/J$ is $\leq d+1$ too.
Key concepts: Square-free integer, Monomial, Mathematics, Polynomial, Combinatorics, Degree (music), Monomial basis, Monomial ideal