TITLE:
Lattice Paths and Rogers Identities
AUTHORS:
Ashok Kumar Agarwal, Megha Goyal
KEYWORDS:
Lattice Paths, Colored Partitions, Generating Functions, Combinatorial Interpretations
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.2,
July
18,
2011
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.