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$n$-color overpartitions, lattice paths, and multiple basic hypergeometric series

Abstract : We define two classes of multiple basic hypergeometric series $V_{k,t}(a,q)$ and $W_{k,t}(a,q)$ which generalize multiple series studied by Agarwal, Andrews, and Bressoud. We show how to interpret these series as generating functions for special restricted lattice paths and for $n$-color overpartitions with weighted difference conditions. We also point out that some specializations of our series can be written as infinite products, which leads to combinatorial identities linking $n$-color overpartitions with ordinary partitions or overpartitions.
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Olivier Mallet. $n$-color overpartitions, lattice paths, and multiple basic hypergeometric series. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.343-356, ⟨10.46298/dmtcs.3643⟩. ⟨hal-01185179⟩



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