Spin-preserving Knuth correspondences for ribbon tableaux
type: Dataset
contact point: Organization
  fn: CCSD
keyword: bijective-proof
keyword: mathmath-comathematics-mathcombinatorics-mathco
keyword: semistandard-ribbon-tableau
keyword: 50000000000
keyword: rsk-correspondence
keyword: infoeu-reposemanticspreprint
keyword: preprints-working-papers-
keyword: spin
landing page: https://hal.science/hal-00000907
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 $\{0,1\}^r$.
issued: 2026-05-08T04:09:39.649019
language: en
modified: 2026-05-08T04:09:39.649022

test_moissonnage_selune
type: Agent

Spin-preserving Knuth correspondences for ribbon tableaux
type: Distribution
access URL: https://hal.science/hal-00000907
format: HTML
issued: 2026-05-08T04:09:39.660527
modified: 2026-05-08T04:09:39.636666