  Recently, fractional Chern insulators (FCIs), also called fractional quantum
anomalous Hall (FQAH) states, have been theoretically established in lattice
systems with topological flat bands. These systems exhibit similar
fractionalization phenomena as the conventional fractional quantum Hall (FQH)
systems. Using the mapping relationship between the FQH states and the FCI/FQAH
states, we construct the many-body wave functions of the fermionic FCI/FQAH
states on the disk geometry with the aid of the generalized Pauli principle
(GPP) and the Jack polynomials. Compared with the ground state by exact
diagonalization method, the wave-function overlap is higher than $0.97$ even
when the Hilbert space dimension is as large as $3\times10^6$. We also use the
GPP and the Jack polynomials to construct edge excitations for the ferminoic
FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems
reproduce the prediction of the chiral Luttinger liquid theory, complementing
the exact diagonalization results with larger lattice sizes and more particles.
