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On q-Series and Split Lattice Paths

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Abstract

In this paper a natural question which arise to study the graphical aspect of split \((n+t)\)-color partitions, is answered by introducing a new class of lattice paths, called split lattice paths. A direct bijection between split \((n+t)\)-color partitions and split lattice paths is proved. This new combinatorial object is applied to give new combinatorial interpretations of two basic functions of Gordon-McIntosh. Some generalized q-series are also discussed. We further explore these paths by providing combinatorial interpretations of some Rogers-Ramanujan type identities which reveal their rich structure and great potential for further research.

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  1. Department of Mathematical Sciences, IK Gujral Punjab Technical University Jalandhar, Main Campus, Kapurthala, 144603, India

    Megha Goyal

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  1. Megha Goyal
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Correspondence to Megha Goyal.

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Goyal, M. On q-Series and Split Lattice Paths. Graphs and Combinatorics 36, 1273–1295 (2020). https://doi.org/10.1007/s00373-020-02207-3

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  • DOI: https://doi.org/10.1007/s00373-020-02207-3

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