Laurent polynomials and Eulerian numbers

Details Laurent polynomials and Eulerian numbers Laurent polynomials and Eulerian numbers

2009-08-18

arxiv.org/abs/0908.2609v2

Journal of Combinatorial Theory, Series A 118 (2011) 396-402

Mathematics

Combinatorics

7 pages; gave a new proof of Lemma 3; made minor corrections and improvements to exposition

Scientific paper

10.1016/j.jcta.2010.02.006

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.

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