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A Tableau Formula of Double Grothendieck Polynomials for 321-Avoiding Permutations

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Abstract

In this article, we prove a tableau formula for the double Grothendieck polynomials associated to 321-avoiding permutations. The proof is based on the compatibility of the formula with the K-theoretic divided difference operators. Our formula specializes to the one obtained by Chen et al. (Eur J Combin 25(8):1181–1196, 2004) for the (double) skew Schur polynomials.

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Acknowledgements

We would like to thank Dave Anderson, Linda Chen, Takeshi Ikeda, Anatol Kirillov for the helpful conversations and their comments. Thanks are also due to the anonymous referee for his/her valuable comments.

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Correspondence to Tomoo Matsumura.

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This work was completed with the support of Grant-in-Aid for Young Scientists (B) 16K17584.

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Matsumura, T. A Tableau Formula of Double Grothendieck Polynomials for 321-Avoiding Permutations. Ann. Comb. (2020). https://doi.org/10.1007/s00026-019-00481-4

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Keywords

  • Symmetric polynomials
  • Grothendieck polynomials
  • K-theory
  • Set-valued tableaux
  • 321-avoiding permutations

Mathematics Subject Classification

  • Primary 05E05
  • Secondary 14M15
  • 05A05