The Zrank Conjecture and Restricted Cauchy Matrices
| dc.creator | Yan, Guo-Guang | |
| dc.creator | Yang, Arthur L. B. | |
| dc.creator | Zhou, Joan J. | |
| dc.date | 2005-04-24 | |
| dc.date.accessioned | 2026-07-07T05:19:23Z | |
| dc.date.available | 2026-07-07T05:19:23Z | |
| dc.description | The 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. | |
| dc.description | 17pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0504488 | |
| dc.identifier | http://arxiv.org/abs/math/0504488 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75001 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E10; 15A15 | |
| dc.title | The Zrank Conjecture and Restricted Cauchy Matrices | |
| dc.type | text |