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ON ROGERS-RAMANUJAN TYPE IDENTITIES FOR OVERPARTITIONS AND GENERALIZED LATTICE PATHS
Goyal, Megha Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
In this paper we introduce and study the lattice paths for which the horizontal step is allowed at height $h{\geq}0$, $h{\in}{\mathbb{Z}}$. 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.
On Rogers--Ramanujan type identities for overpartitions and generalized lattice paths
Megha Goyal 대한수학회 2018 대한수학회보 Vol.55 No.2
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.
Singh Jaspal,Kaur Kulwinder,Islam Ishtihadah,Mir Jan Mohammad,Goyal Megha,Kaur Tavneet,Verma S.S.,Ali Atif Mossad,Khandy Shakeel Ahmad 한국물리학회 2023 Current Applied Physics Vol.50 No.-
This paper presents a detailed discussion of thermoelectric and electronic properties of newly designed Li-based Heusler compounds (LiScPtGe, LiYPtSn, LiYPdPb) using Boltzmann transport theory alongside the first-principles calculations. Our investigations predict that these materials exhibit band gaps 0.76 eV (for LiScPtGe), 0.67 (for LiYPtGe) and 0.21 eV (for LiYPdPb), respectively. All the reported materials are indirect band gap semiconductors; mechanical and dynamical stability is also confirmed. At 300 K, the lowest value of lattice thermal conductivity is observed in LiYPdPb (21.64 Wm-1 K-1), which is very small as compared to the other two materials. The perceived value of the figure of merit (ZT) is 0.61 (for LiScPtGe), 0.52 (for LiYPtSn) and 0.35 (for LiYPdPb) respectively, and probably ensure a considerable thermoelectric efficiency of these newly designed materials.