A $q$-Robinson-Schensted-Knuth Algorithm and a $q$-Polymer

@article{Pei2017AA,
  title={A \$q\$-Robinson-Schensted-Knuth Algorithm and a \$q\$-Polymer},
  author={Y. Pei},
  journal={Electron. J. Comb.},
  year={2017},
  volume={24},
  pages={P4.6}
}
  • Y. Pei
  • Published 2017
  • Mathematics, Computer Science
  • Electron. J. Comb.
In [Matveev-Petrov 2016](arXiv:1504.00666) a $q$-deformed Robinson-Schensted-Knuth algorithm ($q$RSK) was introduced. In this article we give reformulations of this algorithm in terms of the Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pairs are swapped in a sense of distribution when the input matrix is transposed. We also formulate a $q$-polymer model based on the $q$RSK, prove the corresponding Burke property… Expand
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