Lattice path moments by cut and paste (Q1398297)

The authors consider lattice paths in the coordinate plane, whose step types consist of \((1,1)\), \((1,-1)\), and possibly of one or more horizontal steps. For the set of such paths running from \((0, 0)\) to \((n+2,0)\) and remaining elsewhere strictly above the horizontal axis, the authors define and study a zeroth moment (cardinality), a first moment (essentially the total area), and a second moment, each in terms of the ordinates of the lattice points traced by the paths. Their main result is a cut and paste bijection, relating these moments to the cardinalities of unrestricted paths running from \((0, 0)\) to \((n, 0)\), which they employ to reestablish known results.