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arXiv · 1812.04390

Identities on Factorial Grothendieck Polynomials

Peter L. Guo·Sophie C. C. Sun
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Abstract

Gustafson and Milne proved an identity on the Schur function indexed by a partition of the form $(\lambda_1-n+k,\lambda_2-n+k,\ldots,\lambda_k-n+k)$. On the other hand, Feh\'{e}r, N\'{e}methi and Rim\'{a}nyi found an identity on the Schur function indexed by a partition of the form $(m-k,\ldots,m-k, \lambda_1,\ldots,\lambda_k)$. Feh\'{e}r, N\'{e}methi and Rim\'{a}nyi gave a geometric explanation of their identity, and they raised the question of finding a combinatorial proof. In this paper, we establish a Gustafson-Milne type identity as well as a Feh\'{e}r-N\'{e}methi-Rim\'{a}nyi type identity for factorial Grothendieck polynomials. Specializing a factorial Grothendieck polynomial to a Schur function, we obtain a combinatorial proof of the Feh\'{e}r-N\'{e}methi-Rim\'{a}nyi identity.

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Peter L. Guo, Sophie C. C. Sun. 2018-12-11. Identities on Factorial Grothendieck Polynomials. https://arxiv.org/abs/1812.04390

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