On Rogers--Ramanujan type identities for overpartitions and generalized lattice paths
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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.
Abstract
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.
참고문헌 (14)
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