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Let $f_1,\cdots,f_r\in k[x_1,\cdots,x_n]$ be homogeneous polynomial of degree$d$. Ananyan and Hochster (2016) proved that there exists a bound $N=N(r,d)$where if collective strength of $f_1,\cdots,f_r\geq N$, then $f_1,\cdots,f_r$are regular sequence. In this paper, we study the explicit bound $N(r,d)$ when$r=3$ and $d=2,3$ and show that $N(3,2)=2$ and $N(3,3)>2$.

Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials