We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies some previous results: it generalizes a combinatorial formula obtained in earlier joint work with López Martín and Teixidor i Bigas concerning Brill–Noether curves, and it generalizes a 2000 formula of Lenart and a recent result of Reiner–Tenner–Yong to skew shapes. We also give an expansion in the other direction: expressing skew Schur functions in terms of skew Grothendieck polynomials.
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Keywords: Schur functions, Grothendieck polynomials, insertion algorithms, set-valued tableaux, Brill–Noether theory.
@article{ALCO_2021__4_1_175_0, author = {Chan, Melody and Pflueger, Nathan}, title = {Combinatorial relations on skew {Schur} and skew stable {Grothendieck} polynomials}, journal = {Algebraic Combinatorics}, pages = {175--188}, publisher = {MathOA foundation}, volume = {4}, number = {1}, year = {2021}, doi = {10.5802/alco.144}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.144/} }
TY - JOUR AU - Chan, Melody AU - Pflueger, Nathan TI - Combinatorial relations on skew Schur and skew stable Grothendieck polynomials JO - Algebraic Combinatorics PY - 2021 SP - 175 EP - 188 VL - 4 IS - 1 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.144/ DO - 10.5802/alco.144 LA - en ID - ALCO_2021__4_1_175_0 ER -
%0 Journal Article %A Chan, Melody %A Pflueger, Nathan %T Combinatorial relations on skew Schur and skew stable Grothendieck polynomials %J Algebraic Combinatorics %D 2021 %P 175-188 %V 4 %N 1 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.144/ %R 10.5802/alco.144 %G en %F ALCO_2021__4_1_175_0
Chan, Melody; Pflueger, Nathan. Combinatorial relations on skew Schur and skew stable Grothendieck polynomials. Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 175-188. doi : 10.5802/alco.144. http://www.numdam.org/articles/10.5802/alco.144/
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