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

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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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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).

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

Mathematics Subject Classification

  • Primary 05E05
  • Secondary 14M15
  • 05A05