Discrete Models: Combinatorics, Computation, and Geometry, DMCCG 2001
Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)
DMTCS Conference Volume AA (2001), pp. 133144
author:  Alberto Del Lungo, Massimo Mirolli, Renzo Pinzani and Simone Rinaldi 

title:  A Bijection for DirectedConvex Polyominoes 
keywords:  cycle lemma, directedconvex polyominoes, binomial coefficients, lattice paths 
abstract: 
In this paper we consider two classes of lattice paths on
the plane which use north, east,
south, and west unitary steps, beginning and
ending at
(0,0)
. We enumerate them according to the number of steps
by means of bijective arguments; in particular, we apply
the cycle lemma. Then, using these results, we provide a
bijective proof for the number of directedconvex
polyominoes having a fixed number of rows and columns.

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reference:  Alberto Del Lungo and Massimo Mirolli and Renzo Pinzani and Simone Rinaldi (2001), A Bijection for DirectedConvex Polyominoes, in Discrete Models: Combinatorics, Computation, and Geometry, DMCCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 133144 
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