Laurent polynomials and Eulerian numbers
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2009
- DOI:
- 10.48550/arXiv.0908.2609
- arXiv:
- arXiv:0908.2609
- Bibcode:
- 2009arXiv0908.2609E
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 05A10;
- 14N15;
- 14M25
- E-Print:
- 7 pages