We obtain an explicit formula to enumerate closed random walks on a cubic lattice with a specified length and algebraic area. The algebraic area of a closed cubic lattice walk is defined as the sum of the algebraic areas obtained from the walk's …
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficients of particles obeying generalized exclusion statistics, and obtain explicit expressions for the counting of paths with a fixed number of steps of …
We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map the problem to a Hofstadter-like Hamiltonian and show that the …