Let be $a(k,m),k,m\geq 0$ an infinite matrix then the set $T_k=\{(a(k,0),a(k,1),...,a(k,i),...),(a(k,0),a(k+1,1),...,a(k+i,i),...)\}$is called angle of matrix
$a(k,0)$ is edge of $T_k$
$a(k,i),a(k+i,i),i>0$ are conjugate elements of $T_k$
$(a(k,0),a(k,1),...,a(k,i),...)$ is horizontal ray of $T_k$
$(a(k,0),a(k+1,1),...,a(k+i,i),...)$is diagonal ray of $T_k$
Elements of diagonal ray of $T_0$ are $1$
Elements above diagonal ray of $T_0$ are $0$
Elements of edge of $T_k,k>0$ are $0$
Each element of diagonal ray of $T_k,k>0$ is sum of his conjugate and elements of horizontal ray of $T_k$ that are placed on left.
Prove that sum of elements of row $k$ is partition function $p(k)$