# Laurent polynomials and Eulerian numbers

@article{Erman2011LaurentPA, title={Laurent polynomials and Eulerian numbers}, author={Daniel Erman and Gregory G. Smith and Anthony V{\'a}rilly-Alvarado}, journal={J. Comb. Theory, Ser. A}, year={2011}, volume={118}, pages={396-402} }

Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels poses two questions: Do the constant terms of a generic Laurent polynomial form a regular sequence? If so, then what is the degree of the associated zero-dimensional ideal? In this note, we prove that the Eulerian numbers provide the answer to the second question. The proof involves reinterpreting the problem in terms of toric… Expand

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Laurent polynomials, Eulerian numbers, and Bernstein's theorem

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