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

dmtcs:3643 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3643
$n$-color overpartitions, lattice paths, and multiple basic hypergeometric seriesArticle

Authors: Olivier Mallet 1

  • 1 Laboratoire d'informatique Algorithmique : Fondements et Applications

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.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: $n$-color overpartitions,lattice paths,multiple series,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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