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