This paper deals with a study of the class P of lattice paths, made of north, east, south, and west unit steps, which being at (-1,0) and end at (0,0), avoiding the non-negative x-axis. P is bijectively proved to be enumerated by odd index Catalan numbers according to the number of steps.
A Bijection for Some Paths on the Slit Plane / E. BARCUCCI; E. PERGOLA; R. PINZANI; S. RINALDI. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - STAMPA. - 26:(2001), pp. 89-96. [10.1006/aama.2000.0709]
A Bijection for Some Paths on the Slit Plane
BARCUCCI, ELENA;PERGOLA, ELISA;PINZANI, RENZO;
2001
Abstract
This paper deals with a study of the class P of lattice paths, made of north, east, south, and west unit steps, which being at (-1,0) and end at (0,0), avoiding the non-negative x-axis. P is bijectively proved to be enumerated by odd index Catalan numbers according to the number of steps.
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