2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113944We prove that the v-decomposition number $d_{λμ}(v)$ is an even or odd polynomial according to whether the partitions $λ$ and $μ$ have the same relative sign (or parity) or not. We then use this result to verify Martin's conjecture for weight 3 blocks of symmetric group algebras -- that these blocks have the property that their projective (indecomposable) modules have a common radical length 7.21 pagesRepresentation TheoryQuantum Algebra17B37; 20C30text