Abstract
Let be the polynomial ring in n variables over a field K and I be a monomial ideal of degree
. We show that
for all
and we disprove a motivation question that was asked by of Carlini, Hà, Harbourne and Van Tuyl by providing of a counterexample. Also, by this counterexample, we give a negative answer to the question that the depth function of square-free monomial ideals are non-increasing.
2020 Mathematics Subject Classification:
Acknowledgments
We would like to thank Kamran Divaani-Aazar and Mehrdad Nasernejad for some helpful comments. Also, we would like to thank deeply grateful to the referee for the careful reading of the manuscript.