Relatório de pesquisa 08/09

New Two-Line Arrays Representing Partitions, José Plínio O. Santos, Paulo Mondek and Andréia C. Ribeiro, submitted March 06, 2009.



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 Lebesgues´ 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 also a complete description for the conjugate partition.

 
Mathematics Subject Classifications (2000): primary 11P81; secondary 05A17

Keywords: 
Partitions, Rogers-Ramanujan identities



If you are interested in obtaining a copy of this Report please contact the author(s) either via e-mail or by snail mail, at the address:
IMECC, UNICAMP
Cx. P. 6065
13083-970 Campinas, SP, BRAZIL

March 10, 2009

 

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