Bull. Korean Math. Soc. 2018; 55(2): 449-467
Online first article March 8, 2018 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b170069
Copyright © The Korean Mathematical Society.
Megha Goyal
I. K. Gujral Punjab Technical University Jalandhar
In this paper we introduce and study the lattice paths for which the horizontal step is allowed at height $h\geq0$, $h\in \mathbb{Z}$. By doing so these paths generalize the heavily studied weighted lattice paths that consist of horizontal steps allowed at height zero only. Six $q$--series identities of Rogers--Ramanujan type are studied combinatorially using these generalized lattice paths. The results are further extended by using $(n+t)$--color overpartitions. Finally, we will establish that there are certain equinumerous families of $(n+t)$--color overpartitions and the generalized lattice paths.
Keywords: \(q\)--series, generalized lattice paths, \((n+t)\)--color overpartitions, combinatorial identities
MSC numbers: Primary 05A15, 05A17, 05A19, 11P81
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd