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Osculating paths are sets of directed lattice paths which are not allowed to cross each other or have common edges, but are allowed to have common vertices. In this work we derive a constant term formula for the number of such lattice paths by solving a set of simultaneous difference equations.
The quantum $tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q rel
A directed path in the vicinity of a hard wall exerts pressure on the wall because of loss of entropy. The pressure at a particular point may be estimated by estimating the loss of entropy if the point is excluded from the path. In this paper we dete
The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.
The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix a
An integrable Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and Dzyaloshinski-Moriya interacton is constructed. The integrability of the model is proven. Based on the Bethe Ansatz solutions, the ground state