Abstract:

Part of MacMahon's partition analysis, or Omega calculus, the constant term operator selects the constant term in a, possibly iterated, Laurent series. MacMahon's methods have recieved some recent attention in combinatorics (mainly by Andrews and co-workers, and Xin), and to a lesser extent in statistical mechanics of polymer models

I will show how constant term methods can be used to solve a weighted lattice path problem, a generalisation of the classical ballot problem. The motivation is to find combinatorial solutions of the Asymmetric Exclusion process, a favourite model in non-equilibrium statistical mechanics (its virtues include a boundary induced face transition, and solvability).