Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities

Alok Shukla

Published 2020-06-06Version 1

We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity and Rogers-Ramanujan identities. A new generalized $ k $-product $q$-series identity is also obtained by employing the tiling-method, wherein the generating function of the set of all possible tilings of a rectangular board is computed in two different ways to obtain the desired $q$-series identity. The tiling-method holds promise for giving an aesthetically pleasing approach to prove old and new $q$-series identities.