Regular Article: A Bijection for Some Paths on the Slit Plane

Authors:
Elena Barcucci;Elisa Pergola;Renzo Pinzani;Simone Rinaldi
Affiliations:
Dipartimento di Sistemi e Informatica, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy;Dipartimento di Sistemi e Informatica, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy;Dipartimento di Sistemi e Informatica, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy;Dipartimento di Sistemi e Informatica, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy
Venue:
Advances in Applied Mathematics
Year:
2001

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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.