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New Two-Line Arrays Representing Partitions
José Plınio O. Santos1, Paulo Mondek2, and Andréia C. Ribeiro3
1Instituto de Matemática, Estatıstíca e Computacäo Científica, Departamento de Matemática Aplicada, Universidade Estadual de Campinas, Cx.P. 6065, 13083-970, Campinas, SP, Brasil
josepli@ime.unicamp.br
2UFMS-DMT, C. Universitária, Cx.P. 549, 79070-900, Campo Grande, MS, Brasil
mondek@dmt.ufms.br
3UFMS-DMT, Campus de Paranaíba, 79500-000, Paranaía, MS, Brasil
acribeiro@nin.ufms.br
Annals of Combinatorics 15 (2) pp.341-354 April, 2011
AMS Subject Classification: 11P81; 05A17
Abstract:
We present combinatorial interpretations for sums into two parameters from which we have, as special cases, combinatorial interpretations for many identities of Slater’s list including Rogers-Ramanujan identities, unrestricted partitions, and Lebesgue’s partition identity. In this work we are representing a number as a vector and providing representation of this vector as a sum of vectors. It is possible to write this representation as a two-line matrix which can be interpreted as lattice paths. We provide three distinct representations for unrestricted partitions. One of them has the property of giving a complete description for the conjugate
partition.
Keywords: partitions, Rogers-Ramanujan identities

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