|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Stanley's Zrank Problem on Skew Partitions | | William Y.C. Chen
; Arthur L.B. Yang
; | | Date: |
8 Sep 2005 | | Subject: | Combinatorics MSC-class: 05E10, 15A15 | math.CO | | Abstract: | We present an affirmative answer to Stanley’s zrank problem, namely, the zrank and rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs depend on the number of zero entries. Similar to notion of the jrank of a skew partition, we give a characterization of the rank in terms of the Giambelli type matrices of the corresponding skew Schur functions. We also show that the sign of the determinant of a factorial Cauchy matrix is uniquely determined by the number of its zero entries, which implies the nonsingularity of the inverse binomial coefficient matrix. | | Source: | arXiv, math.CO/0509181 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER