Combinatorial proofs of Ramanujanʹs 1ψ1 summation and the q-Gauss summation

Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using F-partitions. In this paper, Ramanujanʹs 1ψ1 summation and the q-Gauss summation are established combinatorially.