Planar Walks with Recursive Initial Conditions

Planar Walks with Recursive Initial Conditions
Abstract We enumerate two-dimensional walks inside a band parallel to an axis of symmetry, using an algebraic approach. The restrictions along the boundary lines can be more complicated than just initial values of zeroes; we consider recursive initial values prescribing which predecessors a position at the boundary can have. More general, the initial conditions are expressed by certain linear operators which vanish along the axis of symmetry.

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