content_image/311449.jpg content_image/311448.jpg
We have four possible q × q submatrices ( with q = 3 ): 

Hence ¯ α = 4 but det ( ˜ G ( y )$_{3}$ ) and det ( ˜ G ( y )$_{4}$ ) are homogeneous polyno- mials of degree 5 > ¯ α. 

<img src='content_image/311449.jpg'>

<img src='content_image/311448.jpg'>

Thus, ¯ α is the smallest possible degree of an homogeneous polynomial in 

