Laurent polynomials and Eulerian numbers

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Erman, Daniel¹  Smith, Gregory G.²  Varilly-Alvarado, Anthony³ 

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

[3] Rice Univ, Dept Math, Houston, TX 77005 USA

关键词: Intersection theory;    Permutations;    Regular sequence;    Toric variety;   

DOI  :  10.1016/j.jcta.2010.02.006

来源: Elsevier

【 摘 要 】

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 geometry. (C) 2010 Daniel Erman. Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free