Particle seas and basic hypergeometric series.
type: Item
instance of: scholarly article
title: Particle seas and basic hypergeometric series.
zbMATH Open document ID: 1050.33010
DOI: 10.1016/S0196-8858(03)00011-3
author: Sylvie Corteel
published in: Advances in Applied Mathematics
publication date: 2003-09-15T00:00:00Z
review text: A particle sea is a geometrical arrangement in the upper half plane, of two types of symbols, say squares and circles, subject to some conditions. Loosely speaking, particle seas are in some sense an analogue of Ferrers graphs from the theory of partitions. The goals of this well written article are to use particle seas to: (i) give a combinatorial proof of Ramanujan's \({}_1\psi_1\) summation formula; (ii) give combinatorial proofs of two special cases of the \({}_6\phi_5\) summation formula, one of which is Heine's \({}_2\phi_1\) \(q\)-analogue of Gauss' \({}_2F_1\) summation formula.
reviewed by: Shaun Cooper
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 1981428
zbMATH Keywords: particle sea
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: bijective proof
zbMATH Keywords: partition
zbMATH Keywords: overpartition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1981428