2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75001The rank of a skew partition $λ/μ$, denoted $rank(λ/μ)$, is the smallest number $r$ such that $λ/μ$ is a disjoint union of $r$ border strips. Let $s_{λ/μ}(1^t)$ denote the skew Schur function $s_{λ/μ}$ evaluated at $x_1=...=x_t=1, x_i=0$ for $i>t$. The zrank of $λ/μ$, denoted $zrank(λ/μ)$, is the exponent of the largest power of $t$ dividing $s_{λ/μ}(1^t)$. Stanley conjectured that $rank(λ/μ)=zrank(λ/μ)$. We show the equivalence between the validity of the zrank conjecture and the nonsingularity of restricted Cauchy matrices. In support of Stanley's conjecture we give affirmative answers for some special cases.17pages, 6 figuresCombinatorics05E10; 15A15text