While studying machine learning, I've read the following statement:
The kernel $K(x,y)=(x\cdot y+1)^d$ , for $x, y \in \mathbb{R}^p$, has $M={p+d \choose d}$ eigenfunctions that span the space of polynomials in $\mathbb{R}^p$ of total degree $d$.
I do not understand how does the $M={p+d \choose d}$ come from? What does exactly the degree $d$ mean here?