Vol. 11, No. 1, 2018

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Coincidences among skew stable and dual stable Grothendieck polynomials

Ethan Alwaise, Shuli Chen, Alexander Clifton, Rebecca Patrias, Rohil Prasad, Madeline Shinners and Albert Zheng

Vol. 11 (2018), No. 1, 143–167
DOI: 10.2140/involve.2018.11.143

The question of when two skew Young diagrams produce the same skew Schur function has been well studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the K-theoretic analogues of the Schur functions. We prove a necessary condition for two skew shapes to give rise to the same dual stable Grothendieck polynomial. We also provide a necessary and sufficient condition in the case where the two skew shapes are ribbons.

symmetric functions, Grothendieck polynomials
Mathematical Subject Classification 2010
Primary: 05E05
Received: 6 October 2016
Accepted: 24 November 2016
Published: 17 July 2017

Communicated by Jim Haglund
Ethan Alwaise
Department of Mathematics and Computer Science
Emory University
Atlanta, GA 30322
United States
Shuli Chen
Cornell University
Ithaca, NY 14850
United States
Alexander Clifton
Massachusetts Institute of Technology
Cambridge, MA 02139
United States
Rebecca Patrias
Université du Québec à Montréal
Montreal QC H2L 2C4
Rohil Prasad
Harvard University
Cambridge, MA 02138
United States
Madeline Shinners
University of Wisconsin-Madison
Madison, WI 53706
United States
Albert Zheng
University of California-Berkeley
Berkeley, CA 94720
United States