Translator Disclaimer
November 2018 Counting the Ideals of Given Codimension of the Algebra of Laurent Polynomials in Two Variables
Christian Kassel, Christophe Reutenauer
Michigan Math. J. 67(4): 715-741 (November 2018). DOI: 10.1307/mmj/1529114453

Abstract

We establish an explicit formula for the number Cn(q) of ideals of codimension (colength) n of the algebra Fq[x,y,x1,y1] of Laurent polynomials in two variables over a finite field Fq of cardinality q. This number is a palindromic polynomial of degree 2n in q. Moreover, Cn(q)=(q1)2Pn(q), where Pn(q) is another palindromic polynomial; the latter is a q-analogue of the sum of divisors of n, which happens to be the number of subgroups of Z2 of index n.

Citation

Download Citation

Christian Kassel. Christophe Reutenauer. "Counting the Ideals of Given Codimension of the Algebra of Laurent Polynomials in Two Variables." Michigan Math. J. 67 (4) 715 - 741, November 2018. https://doi.org/10.1307/mmj/1529114453

Information

Received: 23 November 2016; Revised: 2 February 2018; Published: November 2018
First available in Project Euclid: 16 June 2018

zbMATH: 07056366
MathSciNet: MR3877434
Digital Object Identifier: 10.1307/mmj/1529114453

Subjects:
Primary: 05A17, 13F20, 14C05, 14N10, 16S34
Secondary: 05A30, 11P84, 11T55, 13P10, 14G15

Rights: Copyright © 2018 The University of Michigan

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.67 • No. 4 • November 2018
Back to Top