3D bosons, 3-Jack polynomials and affine Yangian of $$ \mathfrak{gl}(1) $$

3D (3 dimensional) Young diagrams are a generalization of 2D diagrams. In this paper, We consider Bosons and 3-Jack polynomials. associate three parameters $h_1,h_2,h_3$ to $y,x,z$-axis respectively. polynomials $P_{n,j}, n\geq j$ with coefficients in $\mathbb C(h_1,h_2,h_3)$, which the Schur functions Jack case. Similar functions, can also be determined by vertex operators Pieri formulas.