2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57664Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: $γ(D+1)=α(D)$ (the exponent describing the singularity of the pressure), and $ν_{\perp}(D+1)=ν(D)$ (the correlation length exponent of the repulsive gas). It also leads to the relation $θ(D+1)=1+σ(D)$, where $σ(D)$ is the Yang-Lee edge exponent. We derive exact expressions for the number of DBP of size N in two dimensions.7 pages, 1 eps figure, ref 24 correctedMathematical PhysicsStatistical Mechanics82B41, 82B27, 82B21, 82B20text