On the combinatorics of modified lattice paths and generalized $q$--series

Meenakshi Rana, Megha Goyal

Abstract


Recently, Agarwal and Sachdeva, 2017, proved two Rogers- Ramanujan type identities for modified lattice paths by establishing a bijection between split (n + t)-color partitions and the modified lattice paths. In this paper, we interpret four generalized basic series combinatorially in terms of modied lattice paths by using a similar bijection. This leads to four new Rogers{Ramanujan type identities for modified lattice paths.


Keywords


$q$--series; split $(n+t)$--color partitions; combinatorial identities; weighted lattice paths; modified lattice paths

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References


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Contributions to Discrete Mathematics. ISSN: 1715-0868