open access

https://hdl.handle.net/2115/83747

G-Tutte Polynomials and Abelian Lie Group Arrangements

英語

2021-01

Oxford University Press

IMRN: International Mathematics Research Notices

2021(1)

152-188

For a list A of elements in a finitely generated abelian group Gamma and an abelian group G, we introduce and study an associated G-Tutte polynomial, defined by counting the number of homomorphisms from associated finite abelian groups to G. The G-Tutte polynomial is a common generalization of the (arithmetic) Tutte polynomial for realizable (arithmetic) matroids, the characteristic quasi-polynomial for integral arrangements, Branden-Moci's arithmetic version of the partition function of an abelian group-valued Potts model, and the modified Tutte-Krushkal-Renhardy polynomial for a finite CW complex. As in the classical case, G-Tutte polynomials carry topological and enumerative information (e.g., the Euler characteristic, point counting, and the Poincare polynomial) of abelian Lie group arrangements. We also discuss differences between the arithmetic Tutte and the G-Tutte polynomials related to the axioms for arithmetic matroids and the (non-)positivity of coefficients.

学術雑誌論文

Accepted Manuscript

This is a pre-copyedited, author-produced version of an article accepted for publication in IMRN: International Mathematics Research Notices following peer review. The version of record Volume 2021, Issue 1, January 2021, Pages 150–188 is available online at: https://doi.org/10.1093/imrn/rnz092

1073-7928