We are considering standard polynomial ring over field.
Let $[x_{ij}]_{i=1,\dots k;j=1,\dots n}$ be $n\times k$ ($n\geq k$) a matrix consisting of random variables. Let's define ideal $I$ as ideal generated by minors $k\times k$ of above matrix. State how many generators has this ideal.
I am not sure if my reasoning is correct. First we need to find number of minors which is ${{n}\choose{k}}$. From these generators we cannot remove any because every monomial of these homogeneous generators is present only once. So all minors are not divisible by each other.
Of course non-zero remain of the division does not indicate that our generator isn't already in the ideal. But construction of Grobner basis out of initial minors would lead to addition (if any) of polynomials with leading terms of higher monomial order.