Laurent polynomials and Eulerian numbers
Combinatorics
2012-07-25 v2 Commutative Algebra
Algebraic Geometry
Abstract
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 posed 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 geometry.
Cite
@article{arxiv.0908.2609,
title = {Laurent polynomials and Eulerian numbers},
author = {Daniel Erman and Gregory G. Smith and Anthony Várilly-Alvarado},
journal= {arXiv preprint arXiv:0908.2609},
year = {2012}
}
Comments
7 pages; gave a new proof of Lemma 3; made minor corrections and improvements to exposition