This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras’ walks; two new non-holonomic classes; and enumer...

The principle of least action seems not to lead equations describing the motion consistent with physical behaviour, for non-holonomic constraints. Here, a response is proposed this fundamental problem in Mathematical Physics. Some considerations are also developed, based on first and second law thermodynamics.

It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of REDUCE are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.

In this paper, control algorithms are presented for formation keeping and path following for non-holonomic platforms. The controls are based on feedback from onboard directional range sensors, and a switching Kalman filter is introduced for active sensing. Stability is analyzed theoretically and robustness is demonstrated in experiments and simulations.