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
Laurent polynomials, Eulerian numbers, and Bernstein's theorem
  • R. Liu
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2014
TLDR
It is shown that a refinement of Eulerian numbers gives a combinatorial interpretation for volumes of certain rational hyperplane sections of the hypercube. Expand

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