On the Hilbert depth of the quotient ring of the edge ideal of a star graph

Silviu Balanescu, Mircea Cimpoeas, Mihai Cipu

Let $S_n=K[x_1,\dots ,x_n,y]$ and $I_n=(x_{1}y,x_{2}y,\dots ,x_{n}y)\subset S_n$ be the edge ideal of star graph. We prove that $\operatorname{hdepth}(S_n/I_n)\geq \left\lceil \frac{n}{2…