# A bijective proof of the Cauchy identity for Grothendieck polynomials

@article{Numata2016ABP, title={A bijective proof of the Cauchy identity for Grothendieck polynomials}, author={Yasuhide Numata}, journal={arXiv: Combinatorics}, year={2016} }

We consider pairs of a set-valued column-strict tableau and a reverse plane partition of the same shape. We introduce algortithms for them, which implies a bijective proof for the finite sum Cauchy identity for Grothendieck polynomials and dual Grothendieck polynomials.

#### References

SHOWING 1-5 OF 5 REFERENCES

Grothendieck classes of quiver varieties

- Mathematics
- 2001

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We… Expand

The Yang-Baxter equation, symmetric functions, and Schubert polynomials

- Mathematics, Computer Science
- Discret. Math.
- 1996

An approach to the theory of Schubert polynomials, corresponding symmetric functions, and their generalizations that is based on exponential solutions of the Yang-Baxter equation is presented. Expand

Combinatorial Expansions in K-Theoretic Bases

- Mathematics, Computer Science
- Electron. J. Comb.
- 2012

The combinatorial description of the coefficients when any element of $\mathcal C$ is expanded in the $G$-basis or the basis dual to $\{G_\lambda\}$. Expand