A quartet of fermionic expressions for M(k,2k ± 1) Virasoro characters via half-lattice paths

We also derive a bosonic version of the generating functions of length L half-lattice paths, this expression being notable in that it involves q-trinomial coefficients. Taking the L→∞ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters χr,sk,2k±1.