Bijections between Lattice Paths and Plane Partitions

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DOI: 10.4236/ojdm.2011.13014   PDF   HTML     5,282 Downloads   9,373 Views   Citations

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 .

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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