OJDM  Vol.1 No.3 , October 2011
Bijections between Lattice Paths and Plane Partitions
ABSTRACT
By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer n in terms of a set of plane partitions of n . We also exhibit two bijections between unrestricted partitions of n and different subsets of plane partitions of n .

Cite this paper
M. Alegri, E. Brietzke, J. Santos and R. Silva, "Bijections between Lattice Paths and Plane Partitions," Open Journal of Discrete Mathematics, Vol. 1 No. 3, 2011, pp. 108-115. doi: 10.4236/ojdm.2011.13014.
References
[1]   P. Mondek, A. C. Ribeiro and J. P. O. Santos, “New Two-Line Arrays Representing Partitions,” Annals of Combinatorics, Vol. 15, No. 2, 2011, pp. 341-354. doi:10.1007/s00026-011-0099-0

[2]   L. J. Slater, “Further Identities of the Rogers-Ramanujan type,” Proc. London Math. Soc., Vol. 54, No. 2, 1952, pp. 147-167. doi:10.1112/plms/s2-54.2.147

[3]   E. H. M. Brietzke, J. P. O. Santos and R. Silva, “Bijective Proofs Using Two-Line Matrix Representations for Partitions,” The Ramanujam Journal, Vol. 23, 2010, pp. 265- 295. doi:10.1007/s11139-009-9207-8

[4]   G. E. Andrews, “Three-Quadrant Ferrers Graphs,” Indian Journal of Mathematics, Vol. 42, 2000, pp. 1-7.

[5]   E. H. M. Brietzke, J. P. O. Santos and R. Silva, “Combinatorial Interpretations as Two-Line Array for the Mock Theta Functions,” Bulletin Brazilian Mathematical Society, Vol. 44, 2013, pp. 233-253.

[6]   M. Alegri, “Interpreta??es para Identidades Envolvendo Sobreparti??es e Parti??es Planas,” Ph.D. Thesis, IME CC-Universidade Estadual de Campinas, Campinas-SP, 2010.

 
 
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