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The states in the irreducible modules of the minimal models can berepresented by infinite lattice paths arising from consideration of thecorresponding RSOS statistical models. For the M(p,2p+1) models, a completelydifferent path representation has been found recently, this one on ahalf-integer lattice; it has no known underlying statistical-modelinterpretation. The correctness of this alternative representation has not yetbeen demonstrated, even at the level of the generating functions, since theresulting fermionic characters differ from the known ones. This gap is filledhere, with the presentation of two versions of a bijection between the two pathrepresentations of the M(p,2p+1) states.  In addition, a half-lattice path representation for the M(p+1,2p+1) models isstated, and other generalisations suggested.

A bijection between paths for the M(p,2p+1) minimal model Virasoro characters