## Algebraically solvable problems: describing polynomials as equivalent to explicit solutions

### Summary

Summary: The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi's Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing some information about the polynomial map P |X1$\times \cdot \cdot \cdot \times$Xn when only incomplete information about the polynomial P (X1, . . . , Xn) is given.

### Mathematics Subject Classification

41A05, 13P10, 05E99, 11C08, 11D79, 05C15, 15A15