Particle seas and basic hypergeometric series.
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.
scientific article; zbMATH DE number 1981428
scientific article