Generalized fermionic discrete Toda hierarchy

We describe bi-Hamiltonian structure and Lax-pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions. Its two reductions—N=4 and N=2 supersymmetric Toda lattice hierarchies—in different (including canonical) bases are investigated. Its r-matrix description, monodromy matrix, and spectral curves are discussed.