Spin-preserving Knuth correspondences for ribbon tableaux
| dc.creator | Van Leeuwen, Marc A. A. | |
| dc.date | 2003-12-01 | |
| dc.date.accessioned | 2026-07-07T05:03:25Z | |
| dc.date.available | 2026-07-07T05:03:25Z | |
| dc.description | The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in ${\bf N}$, and standard Young tableaux by semistandard ones. For $r>0$, the Robinson-Schensted correspondence can be trivially extended, using the $r$-quotient map, to one between coloured permutations and pairs of standard $r$-ribbon tableaux built on a fixed $r$-core (the Stanton-White correspondence). This correspondence can also be generalised to arbitrary matrices with entries in ${\bf N}^r$ and pairs of semistandard $r$-ribbon tableaux built on a fixed $r$-core; the generalisation is derived from the RSK correspondence, again using the $r$-quotient map. Shimozono and White recently defined a more interesting generalisation of the Robinson-Schensted correspondence to coloured permutations and standard $r$-ribbon tableaux, one that (unlike the Stanton-White correspondence) respects the spin statistic (total height of ribbons) on standard $r$-ribbon tableaux, relating it directly to the colours of the coloured permutation. We define a construction establishing a bijective correspondence between general matrices with entries in ${\bf N}^r$ and pairs of semistandard $r$-ribbon tableaux built on a fixed $r$-core, which respects the spin statistic on those tableaux in a similar manner, relating it directly to the matrix entries. We also define a similar generalisation of the asymmetric RSK correspondence, in which case the matrix entries are taken from $\{0,1\}^r$. | |
| dc.identifier | https://arxiv.org/abs/math/0312020 | |
| dc.identifier | http://arxiv.org/abs/math/0312020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69411 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E10 | |
| dc.title | Spin-preserving Knuth correspondences for ribbon tableaux | |
| dc.type | text |