Bijections between Lattice Paths and Plane Partitions

Author(s)
Mateus Alegri,
Eduardo Henrique de Mattos Brietzke,
José Plínio de Oliveira Santos,
Robson da Silva

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* .

By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer

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.

M. Alegri, E. Brietzke, J. Santos and R. Silva, "Bijections between Lattice Paths and Plane Partitions,"

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.

[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.