Proceedings of the 13th WSEAS International Conference on APPLIED MATHEMATICS (MATH'08) Encoding properties of Lukasiewics paths

摘要

Lukasiewics paths - lattice paths on non-negative integers with up-steps by arbitrary number of units but down-steps of one unit - have recursive features, reflected in that their generating function is expressed as a gen-eralized continued fraction. Moveover, Lukasiewics paths can be used to construct various familiar combinatorial objects: permutations, partitions, idempotent functions, and multipermutations. The construction procedures lead to representations of the generating functions of these familiar objects as generalized continued fractions.