Lattice Paths and Rogers Identities

Ashok Kumar Agarwal, Megha Goyal

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DOI: 10.4236/ojdm.2011.12011                

Abstract

Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n +t cop-ies of n” of Agarwal and Andrews (J. Combin. Theory Ser.A, 45(1987), No.1, 40-49). In this paper we use lattice paths of Agarwal and Bressoud (Pacific J. Math. 136(2) (1989), 209-228) to provide new combinatorial interpretations of the same identities. This results in five new 3-way combinatorial identities.

Keywords

Lattice Paths, Colored Partitions, Generating Functions, Combinatorial Interpretations

Conflicts of Interest

The authors declare no conflicts of interest.

References

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