In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems.[1] The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz,[2] have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed.
^Guth, L. (2016). Polynomial Methods in Combinatorics. University Lecture Series. American Mathematical Society. ISBN 978-1-4704-2890-7. Retrieved 2019-12-11.
^Alon, Noga (1999). "Combinatorial Nullstellensatz". Combinatorics, Probability and Computing. 8 (1–2): 7–29. doi:10.1017/S0963548398003411. ISSN 0963-5483. S2CID 209877602.
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