Exotic Bailey-Slater SPT-functions I: Group A

We introduce several spt-type functions that arise from Bailey pairs. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are constructed by adding an extra variable z into the generating functions. We find dissections when z is a certain root of unity, as has been done for many rank and crank difference formulas of various partition type objects. Our formulas require an identity of S.H. Chan on generalized Lambert series.