  The Gordon-Andrews identities, which generalize the Rogers-Ramanujan-Schur
identities, provide product and fermionic forms for the characters of the
minimal conformal field theories (CFTs) M(2,2k+1). We discuss/conjecture
identities of a similar type, providing two different fermionic forms for the
characters of the models SM(2,4k) in the minimal series of N=1 super-CFTs.
These two forms are related to two families of thermodynamic Bethe Ansatz (TBA)
systems, which are argued to be associated with the $\hat{\phi}_{1,3}^{\rm
top}$- and $\hat{\phi}_{1,5}^{\rm bot}$-perturbations of the models SM(2,4k).
Certain other q-series identities and TBA systems are also discussed, as well
as a possible representation-theoretical consequence of our results, based on
Andrews's generalization of the Gollnitz-Gordon theorem.
